Accessibility navigation

Bergman spaces with exponential type weights

Arroussi, H. (2021) Bergman spaces with exponential type weights. Journal of Inequalities and Applications, 2021 (1). 193. ISSN 1029-242X

Text (Open Access) - Published Version
· Available under License Creative Commons Attribution.
· Please see our End User Agreement before downloading.


It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

To link to this item DOI: 10.1186/s13660-021-02726-4


Abstract: For 1≤p<∞, let Aωp be the weighted Bergman space associated with an exponential type weight ω satisfying ∫D|Kz(ξ)|ω(ξ)1/2dA(ξ)≤Cω(z)−1/2, z∈D, where Kz is the reproducing kernel of Aω2. This condition allows us to obtain some interesting reproducing kernel estimates and more estimates on the solutions of the ∂̅-equation (Theorem 2.5) for more general weight ω∗. As an application, we prove the boundedness of the Bergman projection on Lωp, identify the dual space of Aωp, and establish an atomic decomposition for it. Further, we give necessary and sufficient conditions for the boundedness and compactness of some operators acting from Aωp into Aωq, 1≤p, q<∞, such as Toeplitz and (big) Hankel operators.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:101825
Uncontrolled Keywords:Review, Bergman space, Bergman kernel, Bergman projection, Atomic decomposition, 32A36, 30H35, 47B38, 41A65, 46J15
Publisher:Springer International Publishing


Downloads per month over past year

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation