Olivia Constantin - Academia.edu (original) (raw)

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Papers by Olivia Constantin

Journal of Mathematical Analysis and Applications, 2015

We show that a dyadic version of the Carleson embedding theorem for the Bergman space extends to ... more We show that a dyadic version of the Carleson embedding theorem for the Bergman space extends to vector-valued functions and operatorvalued measures. This is in contrast to a result by Nazarov, Treil, Volberg in the context of the Hardy space. We also discuss some embeddings for analytic vector-valued functions.

... E-mail addresses: aleman@maths.lth.se (A. Aleman), olivia.constantin@univie.ac.at (O. Constan... more ... E-mail addresses: aleman@maths.lth.se (A. Aleman), olivia.constantin@univie.ac.at (O. Constantin).22-1236/$ â€“ see front matter ï›™ 2011 Elsevier Inc. ... AID:6269 /FLA [m1+; v 1.136; Prn:13/12/2011; 15:37] P.2 (1-20) 2 pr fo w M ww ge in w ch D ba It pr re fo th (1 (2 F no It isA. ...

ABSTRACT We consider Foguel-Hankel operators on vector-valued Bergman spaces. Such operators defi... more ABSTRACT We consider Foguel-Hankel operators on vector-valued Bergman spaces. Such operators defined on Hardy spaces play a central role in the famous example by Pisier of a polynomially bounded operator which is not similar to a contraction. On Bergman spaces we encounter a completely different behaviour; power boundedness, polynomial boundedness, and similarity to a contraction are all equivalent for this class of operators.

Bulletin des Sciences Mathématiques, 2014

ABSTRACT Let v(r)=exp⁡(−α1−r) with α>0α>0, and let DD be the unit disc in the compl... more ABSTRACT Let v(r)=exp⁡(−α1−r) with α>0α>0, and let DD be the unit disc in the complex plane. Denote by Avp the subspace of analytic functions of Lp(D,v)Lp(D,v) and let PvPv be the orthogonal projection from L2(D,v)L2(D,v) onto Av2. In 2004, Dostanic revealed the intriguing fact that PvPv is bounded from Lp(D,v)Lp(D,v) to Avp only for p=2p=2, and he posed the related problem of identifying the duals of Avp for p≥1p≥1, p≠2p≠2. In this paper we propose a solution to this problem by proving that that PvPv is bounded from Lp(D,vp/2)Lp(D,vp/2) to Avp/2p whenever 1≤p<∞1≤p<∞, and, consequently, the dual of Avp/2p for p≥1p≥1 can be identified with Avq/2q, where 1/p+1/q=11/p+1/q=1. In addition, we also address a similar question on some classes of weighted Fock spaces.

The Journal of Geometric Analysis, 2015

We obtain a complete characterization of the entire functions g such that the integral operator (... more We obtain a complete characterization of the entire functions g such that the integral operator (Tgf )(z) = z 0 f (ζ) g ′ (ζ) dζ is bounded or compact, on a large class of Fock spaces F φ p , induced by smooth radial weights that decay faster than the classical Gaussian one. In some respects, these spaces turn out to be significantly different than the classical Fock spaces. Descriptions of Schatten class integral operators are also provided.

Nonlinear Analysis: Real World Applications, 2014

ABSTRACT We provide sufficient conditions under which the unique solution to a nonlinear integral... more ABSTRACT We provide sufficient conditions under which the unique solution to a nonlinear integral equation of convolution type is monotonic. As a consequence, we obtain information about the asymptotic behaviour of the solution in situations where previous results fail to apply.

Nonlinear Analysis: Theory, Methods & Applications, 2008

ABSTRACT For a class of nonlinear integral equations of convolution type we give necessary and su... more ABSTRACT For a class of nonlinear integral equations of convolution type we give necessary and sufficient conditions for the boundedness of nonnegative solutions. Moreover, conditions for the solution to converge asymptotically to a determined limit are obtained.

Journal of Mathematical Analysis and Applications, 2000

We prove a Gronwall-like inequality and present some of its applications to the qualitative study... more We prove a Gronwall-like inequality and present some of its applications to the qualitative study of retarded differential equations. The problems of global continuation of the solutions and the existence of nonoscillatory solutions are considered. By means of examples we show the usefulness of our results.

Journal of Mathematical Analysis and Applications, 2006

Integral inequalities are very useful in the qualitative analysis of differential and integral eq... more Integral inequalities are very useful in the qualitative analysis of differential and integral equations. Starting with [O. Lipovan, A retarded Gronwall-like inequality and its applications, J. Math. Anal. Appl. 252 (2000) 389-401], several recent investigations, see [O. Lipovan, A retarded integral inequality and its applications, ], were devoted to retarded integral inequalities. In this paper we consider the case of retarded Volterra integral equations. We establish bounds on the solutions and, by means of examples, we show the usefulness of our results in investigating the asymptotic behaviour of the solutions.

Journal of Mathematical Analysis and Applications, 2003

We prove a retarded nonlinear integral inequality and present some applications of it to the glob... more We prove a retarded nonlinear integral inequality and present some applications of it to the global existence of solutions to differential equations with time delay.

Journal of Functional Analysis, 2009

We investigate pairs of commuting Foias-Williams/Peller type operators acting on vector-valued we... more We investigate pairs of commuting Foias-Williams/Peller type operators acting on vector-valued weighted Bergman spaces. We prove that a commuting pair of such operators is jointly polynomially bounded if and only if it is similar to a pair of contractions, if and only if both operators are polynomially bounded.

Journal of Functional Analysis, 2012

ABSTRACT We characterize the boundedness of the Bergman projection on vector-valued L2L2-spaces w... more ABSTRACT We characterize the boundedness of the Bergman projection on vector-valued L2L2-spaces with operator-valued weights in terms of an appropriate condition of Muckenhoupt-type for the weight. This contrasts with the situation on Hardy spaces, where such characterizations are only possible in the finite-dimensional case.

Journal d'Analyse Mathématique, 2009

Bulletin of the London Mathematical Society, 2005

Journal of Mathematical Analysis and Applications, 2011

We characterize the Schatten class membership of the canonical solution operator to∂ acting on L ... more We characterize the Schatten class membership of the canonical solution operator to∂ acting on L 2 (e −2φ ), where φ is a subharmonic function with ∆φ a doubling measure. The obtained characterization is in terms of ∆φ. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in L 2 (e −2φ ).