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Papers by José García-Cuerva

Research paper thumbnail of An Extrapolation Theorem in the Theory of A p Weights

Proceedings of the American Mathematical Society, Mar 1, 1983

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Research paper thumbnail of Weighted norm inequalities for commutators of strongly singular integrals

Indiana University Mathematics Journal, 1991

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Research paper thumbnail of Неравенство Хаусдорфа - Юнга с векторнозначными коэффициентами и приложения

Uspehi matematičeskih nauk, 1998

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Research paper thumbnail of Spline Wavelet Bases of Weighted L p Spaces, 1 ≤p < ∞

Proceedings of the American Mathematical Society, Feb 1, 1995

We study necessary conditions on the weight w for the spline wavelet systems to be bases in the w... more We study necessary conditions on the weight w for the spline wavelet systems to be bases in the weighted space LP (w) . In this article we study some questions arising in the investigation of the prob- lem of describing those classes of weight functions w for which the wavelet systems are bases or unconditional bases in the weighted spaces LP (w) = LP(R, w). A priori these conditions depend on the concrete system. But there are some features which are common to all wavelet systems. Here we examine only the case of spline wavelet systems defined on the real line R. For a given non-negative integer m, the spline wavelets are defined in the following way: Let V0 = {f E L2(R) n Cm-l(R) such that the restriction of f to each interval )n, n + 1 ( is a polynomial of degree < m}, where by C (R) we denote the class of functions on R whose derivatives of order r are continuous and by C-' (R) we denote the class of piecewise continuous functions on R. Defining Vj+j = {f(2x) : f(x) E Vj} , we get a multiscale analysis of L2(R) in the sense of Mallat and Meyer (see (M), (D)).

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Research paper thumbnail of Weighted H p spaces

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Research paper thumbnail of José Luis Rubio de Francia (1949-1988)

Collectanea Mathematica

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Research paper thumbnail of Desigualdades con pesos en el Análisis de Fourier de los espacios de tipo homogéneo a las medidas no doblantes

Tesis doctoral inédita. Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Mat... more Tesis doctoral inédita. Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Matemáticas, Fecha de lectura: 25-05-2001

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Research paper thumbnail of Theory of weights and functions of bounded mean oscillation

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Research paper thumbnail of The work of José Luis Rubio de Francia (II)

Publicacions Matematiques

I am going to discuss the work José Luis Rubio did on weighted norm inequalities. Most of it is i... more I am going to discuss the work José Luis Rubio did on weighted norm inequalities. Most of it is in the book we wrote together on the subject [12].

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Research paper thumbnail of Una teoría de espacios de Hardy con átomos locales

Tesis doctoral inédita. Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Mat... more Tesis doctoral inédita. Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Matemáticas. Fecha de lectura: 30-6-94

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Research paper thumbnail of Proceedings of the 5th conference on harmonic analysis and partial differential equations, El Escorial, Spain, June 17–20, 1996 dedicated to Professor Miguel de Guzmán on the occasion of his 60th birthday

Journal of Fourier Analysis and Applications

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Research paper thumbnail of ActaMatHun

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Research paper thumbnail of Conjugate system characterizations of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>H</mi><mn>1</mn></msup></mrow><annotation encoding="application/x-tex">H^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" style="margin-right:0.08125em;">H</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">1</span></span></span></span></span></span></span></span></span></span></span>: Counter examples for the Euclidean plane and local fields

Bulletin of the American Mathematical Society, 1976

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Research paper thumbnail of On the existence of principal values for the cauchy integral on weighted lebesgue spaces for non-doubling measures

The Journal of Fourier Analysis and Applications, 2001

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Research paper thumbnail of On Men'shov's C-strong property

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Research paper thumbnail of Spline wavelet bases of weighted spaces

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Research paper thumbnail of Spline Wavelet Bases of Weighted Lp Spaces

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Research paper thumbnail of Wavelet characterization of weighted spaces

Journal of Geometric Analysis, 2001

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Research paper thumbnail of Calderón-Zygmund operators and unconditional bases of weighted Hardy spaces

Studia Mathematica, 1994

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Research paper thumbnail of Vector-valued Hausdorff-Young inequality and applications

Russian Mathematical Surveys, 1998

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Research paper thumbnail of An Extrapolation Theorem in the Theory of A p Weights

Proceedings of the American Mathematical Society, Mar 1, 1983

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Research paper thumbnail of Weighted norm inequalities for commutators of strongly singular integrals

Indiana University Mathematics Journal, 1991

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Research paper thumbnail of Неравенство Хаусдорфа - Юнга с векторнозначными коэффициентами и приложения

Uspehi matematičeskih nauk, 1998

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Research paper thumbnail of Spline Wavelet Bases of Weighted L p Spaces, 1 ≤p < ∞

Proceedings of the American Mathematical Society, Feb 1, 1995

We study necessary conditions on the weight w for the spline wavelet systems to be bases in the w... more We study necessary conditions on the weight w for the spline wavelet systems to be bases in the weighted space LP (w) . In this article we study some questions arising in the investigation of the prob- lem of describing those classes of weight functions w for which the wavelet systems are bases or unconditional bases in the weighted spaces LP (w) = LP(R, w). A priori these conditions depend on the concrete system. But there are some features which are common to all wavelet systems. Here we examine only the case of spline wavelet systems defined on the real line R. For a given non-negative integer m, the spline wavelets are defined in the following way: Let V0 = {f E L2(R) n Cm-l(R) such that the restriction of f to each interval )n, n + 1 ( is a polynomial of degree < m}, where by C (R) we denote the class of functions on R whose derivatives of order r are continuous and by C-' (R) we denote the class of piecewise continuous functions on R. Defining Vj+j = {f(2x) : f(x) E Vj} , we get a multiscale analysis of L2(R) in the sense of Mallat and Meyer (see (M), (D)).

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Research paper thumbnail of Weighted H p spaces

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Research paper thumbnail of José Luis Rubio de Francia (1949-1988)

Collectanea Mathematica

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Research paper thumbnail of Desigualdades con pesos en el Análisis de Fourier de los espacios de tipo homogéneo a las medidas no doblantes

Tesis doctoral inédita. Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Mat... more Tesis doctoral inédita. Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Matemáticas, Fecha de lectura: 25-05-2001

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Research paper thumbnail of Theory of weights and functions of bounded mean oscillation

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Research paper thumbnail of The work of José Luis Rubio de Francia (II)

Publicacions Matematiques

I am going to discuss the work José Luis Rubio did on weighted norm inequalities. Most of it is i... more I am going to discuss the work José Luis Rubio did on weighted norm inequalities. Most of it is in the book we wrote together on the subject [12].

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Research paper thumbnail of Una teoría de espacios de Hardy con átomos locales

Tesis doctoral inédita. Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Mat... more Tesis doctoral inédita. Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Matemáticas. Fecha de lectura: 30-6-94

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Research paper thumbnail of Proceedings of the 5th conference on harmonic analysis and partial differential equations, El Escorial, Spain, June 17–20, 1996 dedicated to Professor Miguel de Guzmán on the occasion of his 60th birthday

Journal of Fourier Analysis and Applications

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Research paper thumbnail of ActaMatHun

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Research paper thumbnail of Conjugate system characterizations of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>H</mi><mn>1</mn></msup></mrow><annotation encoding="application/x-tex">H^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" style="margin-right:0.08125em;">H</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">1</span></span></span></span></span></span></span></span></span></span></span>: Counter examples for the Euclidean plane and local fields

Bulletin of the American Mathematical Society, 1976

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Research paper thumbnail of On the existence of principal values for the cauchy integral on weighted lebesgue spaces for non-doubling measures

The Journal of Fourier Analysis and Applications, 2001

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Research paper thumbnail of On Men'shov's C-strong property

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Research paper thumbnail of Spline wavelet bases of weighted spaces

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Research paper thumbnail of Spline Wavelet Bases of Weighted Lp Spaces

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Research paper thumbnail of Wavelet characterization of weighted spaces

Journal of Geometric Analysis, 2001

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Research paper thumbnail of Calderón-Zygmund operators and unconditional bases of weighted Hardy spaces

Studia Mathematica, 1994

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Research paper thumbnail of Vector-valued Hausdorff-Young inequality and applications

Russian Mathematical Surveys, 1998

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