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Université Sorbonne Paris Nord / Sorbonne Paris Nord University

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Papers by S. Kwapien

Research paper thumbnail of Séminaire Équations aux dérivées partielles–École Polytechnique

Volume des ensembles nodaux des fonctions propres du laplacien Séminaire Équations aux dérivées p... more Volume des ensembles nodaux des fonctions propres du laplacien Séminaire Équations aux dérivées partielles (Polytechnique) (1984-1985), exp. n o 14, p. 1-9. <http://www.numdam.org/item?id=SEDP_1984-1985____A14_0> © Séminaire Équations aux dérivées partielles (École Polytechnique), 1984-1985, tous droits réservés. L'accès aux archives du séminaire Équations aux dérivées partielles (http://sedp.cedram.org) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

Research paper thumbnail of COMMUNICATIONS in PROBABILITY A PROOF OF A CONJECTURE OF BOBKOV AND HOUDRE

S.G. Bobkov and C. Houdre recently posed the following question on the Internet ([1]): Let X, Y b... more S.G. Bobkov and C. Houdre recently posed the following question on the Internet ([1]): Let X, Y be symmetric i.i.d. random variables such that: IPf jX + Y jp 2 tg IPfjXj tg; for each t> 0. Does it follow that X has nite second moment (which then easily implies that X is Gaussian)? In this note we give an armative answer to this problem and present a proof. Using a dierent method K. Oleszkiewicz has found another proof of this conjecture, as well as further related results. We prove the following: Theorem. Let X, Y be symmetric i.i.d random variables. If, for each t> 0, IPfjX + Y j p2tg IPfjXj tg; (1) then X is Gaussian. Proof. Step 1. IEfjXjpg <1 for 0 p < 2. For this purpose it will suce to show that, for p < 2, X has nite weak p’th moment, i.e., that there are constants Cp such that IPfjXj tg Cpt−p: To do so, it is enough to show that, for > 0; > 0, we can nd t0 such that, for t t0, we have 7

Research paper thumbnail of AMS 1991 Subject classification: 60E05 Keywords and phrases: Gaussian Distribution, Characterization

Research paper thumbnail of Enflo's example of a Banach space without the approximation property

École Polytechnique), 1972-1973, tous droits réservés. L'accès aux archives du séminaire Équation... more École Polytechnique), 1972-1973, tous droits réservés. L'accès aux archives du séminaire Équations aux dérivées partielles (http://sedp.cedram.org) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

Research paper thumbnail of Font Size User

Research paper thumbnail of Sums of independent Banach space valued random variables (after J. Hoffmann-Jørgensen)

Research paper thumbnail of Comments to Enflo's construction of Banach space without the approximation property

© Séminaire Équations aux dérivées partielles (Polytechnique) (École Polytechnique), 1972-1973, t... more © Séminaire Équations aux dérivées partielles (Polytechnique) (École Polytechnique), 1972-1973, tous droits réservés. L’accès aux archives du séminaire Équations aux dérivées partielles (http://sedp.cedram.org) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Research paper thumbnail of Isomorphic characterizations of Hilbert spaces by orthogonal series with vector valued coefficients

© Séminaire analyse fonctionnelle (dit "Maurey-Schwartz") (École Polytechnique), 1972-1... more © Séminaire analyse fonctionnelle (dit "Maurey-Schwartz") (École Polytechnique), 1972-1973, tous droits réservés. L’accès aux archives du séminaire d’analyse fonctionnelle implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Research paper thumbnail of On some conjecture concerning Gaussian measures of dilatations of convex symmetric sets

Research paper thumbnail of An estimation of the Lebesgue functions of biorthogonal systems with an application to the non-existence of some bases in C and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>L</mi><mn>1</mn></msup></mrow><annotation encoding="application/x-tex">L^{1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span>

Research paper thumbnail of A remark on p-absolutely summing operators in <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>l</mi><mi>r</mi></msub></mrow><annotation encoding="application/x-tex">l_{r}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0197em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>-spaces

Research paper thumbnail of On Banach spaces containing <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>c</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">c_{0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>. A supplement to the paper by J.Hoffman-Jørgensen "Sums of independent Banach space valued random variables

Research paper thumbnail of Sums of independent Banach space valued random variables

Research paper thumbnail of Random Series and Stochastic Multiple Integrals: Single and Multiple

Research paper thumbnail of On Operators Factorizable Through L Space P

Research paper thumbnail of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi></mrow><annotation encoding="application/x-tex">R</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span></span></span></span>-boundedness versus $ gamma$-boundedness

It is well-known that in Banach spaces with finite cotype, the R-bounded and γbounded families of... more It is well-known that in Banach spaces with finite cotype, the R-bounded and γbounded families of operators coincide. If in addition X is a Banach lattice, then these notions can be expressed as square function estimates. It is also clear that R-boundedness implies γboundedness. In this note we show that all other possible inclusions fail. Furthermore, we will prove that R-boundedness is stable under taking adjoints if and only if the underlying space is K-convex.

Research paper thumbnail of The LIL for canonical Uu-statistics of order 2

Annals of Probability, 2001

Research paper thumbnail of On Banach spaces containing c0

Research paper thumbnail of Remarks on absolutely summing translation invariant operators from the disc algebra and its dual into a Hilbert space

The Michigan Mathematical Journal, 1978

Research paper thumbnail of Regularity of solutions of linear stochastic equations in hilbert spaces

Stochastics, 1988

The paper gives sufficient, and in some cases necessary and sufficient, conditions for the mild s... more The paper gives sufficient, and in some cases necessary and sufficient, conditions for the mild solution of a stochastic linear equation to be regular both &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;quot;in time&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;quot; and &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;quot;in space&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;quot; or to be the strong solution

Research paper thumbnail of Séminaire Équations aux dérivées partielles–École Polytechnique

Volume des ensembles nodaux des fonctions propres du laplacien Séminaire Équations aux dérivées p... more Volume des ensembles nodaux des fonctions propres du laplacien Séminaire Équations aux dérivées partielles (Polytechnique) (1984-1985), exp. n o 14, p. 1-9. <http://www.numdam.org/item?id=SEDP_1984-1985____A14_0> © Séminaire Équations aux dérivées partielles (École Polytechnique), 1984-1985, tous droits réservés. L'accès aux archives du séminaire Équations aux dérivées partielles (http://sedp.cedram.org) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

Research paper thumbnail of COMMUNICATIONS in PROBABILITY A PROOF OF A CONJECTURE OF BOBKOV AND HOUDRE

S.G. Bobkov and C. Houdre recently posed the following question on the Internet ([1]): Let X, Y b... more S.G. Bobkov and C. Houdre recently posed the following question on the Internet ([1]): Let X, Y be symmetric i.i.d. random variables such that: IPf jX + Y jp 2 tg IPfjXj tg; for each t> 0. Does it follow that X has nite second moment (which then easily implies that X is Gaussian)? In this note we give an armative answer to this problem and present a proof. Using a dierent method K. Oleszkiewicz has found another proof of this conjecture, as well as further related results. We prove the following: Theorem. Let X, Y be symmetric i.i.d random variables. If, for each t> 0, IPfjX + Y j p2tg IPfjXj tg; (1) then X is Gaussian. Proof. Step 1. IEfjXjpg <1 for 0 p < 2. For this purpose it will suce to show that, for p < 2, X has nite weak p’th moment, i.e., that there are constants Cp such that IPfjXj tg Cpt−p: To do so, it is enough to show that, for > 0; > 0, we can nd t0 such that, for t t0, we have 7

Research paper thumbnail of AMS 1991 Subject classification: 60E05 Keywords and phrases: Gaussian Distribution, Characterization

Research paper thumbnail of Enflo's example of a Banach space without the approximation property

École Polytechnique), 1972-1973, tous droits réservés. L'accès aux archives du séminaire Équation... more École Polytechnique), 1972-1973, tous droits réservés. L'accès aux archives du séminaire Équations aux dérivées partielles (http://sedp.cedram.org) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

Research paper thumbnail of Font Size User

Research paper thumbnail of Sums of independent Banach space valued random variables (after J. Hoffmann-Jørgensen)

Research paper thumbnail of Comments to Enflo's construction of Banach space without the approximation property

© Séminaire Équations aux dérivées partielles (Polytechnique) (École Polytechnique), 1972-1973, t... more © Séminaire Équations aux dérivées partielles (Polytechnique) (École Polytechnique), 1972-1973, tous droits réservés. L’accès aux archives du séminaire Équations aux dérivées partielles (http://sedp.cedram.org) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Research paper thumbnail of Isomorphic characterizations of Hilbert spaces by orthogonal series with vector valued coefficients

© Séminaire analyse fonctionnelle (dit "Maurey-Schwartz") (École Polytechnique), 1972-1... more © Séminaire analyse fonctionnelle (dit "Maurey-Schwartz") (École Polytechnique), 1972-1973, tous droits réservés. L’accès aux archives du séminaire d’analyse fonctionnelle implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Research paper thumbnail of On some conjecture concerning Gaussian measures of dilatations of convex symmetric sets

Research paper thumbnail of An estimation of the Lebesgue functions of biorthogonal systems with an application to the non-existence of some bases in C and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>L</mi><mn>1</mn></msup></mrow><annotation encoding="application/x-tex">L^{1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span>

Research paper thumbnail of A remark on p-absolutely summing operators in <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>l</mi><mi>r</mi></msub></mrow><annotation encoding="application/x-tex">l_{r}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0197em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>-spaces

Research paper thumbnail of On Banach spaces containing <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>c</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">c_{0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>. A supplement to the paper by J.Hoffman-Jørgensen "Sums of independent Banach space valued random variables

Research paper thumbnail of Sums of independent Banach space valued random variables

Research paper thumbnail of Random Series and Stochastic Multiple Integrals: Single and Multiple

Research paper thumbnail of On Operators Factorizable Through L Space P

Research paper thumbnail of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi></mrow><annotation encoding="application/x-tex">R</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span></span></span></span>-boundedness versus $ gamma$-boundedness

It is well-known that in Banach spaces with finite cotype, the R-bounded and γbounded families of... more It is well-known that in Banach spaces with finite cotype, the R-bounded and γbounded families of operators coincide. If in addition X is a Banach lattice, then these notions can be expressed as square function estimates. It is also clear that R-boundedness implies γboundedness. In this note we show that all other possible inclusions fail. Furthermore, we will prove that R-boundedness is stable under taking adjoints if and only if the underlying space is K-convex.

Research paper thumbnail of The LIL for canonical Uu-statistics of order 2

Annals of Probability, 2001

Research paper thumbnail of On Banach spaces containing c0

Research paper thumbnail of Remarks on absolutely summing translation invariant operators from the disc algebra and its dual into a Hilbert space

The Michigan Mathematical Journal, 1978

Research paper thumbnail of Regularity of solutions of linear stochastic equations in hilbert spaces

Stochastics, 1988

The paper gives sufficient, and in some cases necessary and sufficient, conditions for the mild s... more The paper gives sufficient, and in some cases necessary and sufficient, conditions for the mild solution of a stochastic linear equation to be regular both &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;quot;in time&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;quot; and &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;quot;in space&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;quot; or to be the strong solution

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