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 doi: 10.1186/s13660-021-02726-4

Abstract/Summary

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
URI	https://reading-clone.eprints-hosting.org/id/eprint/101825
Identification Number/DOI	10.1186/s13660-021-02726-4
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Uncontrolled Keywords	Review, Bergman space, Bergman kernel, Bergman projection, Atomic decomposition, 32A36, 30H35, 47B38, 41A65, 46J15
Publisher	Springer International Publishing
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