Weighted Bergman Spaces Induced By Rapidly Increasing Weights
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Weighted Bergman Spaces Induced by Rapidly Increasing Weights
January 2014, volume 227, number 1066 (second of 4 numbers).
Weighted Bergman Spaces Induced by Rapidly Increasing Weights
Author: Jose Angel Pelaez
language: en
Publisher: American Mathematical Soc.
Release Date: 2014-01-08
This monograph is devoted to the study of the weighted Bergman space $A^p_\omega$ of the unit disc $\mathbb{D}$ that is induced by a radial continuous weight $\omega$ satisfying $\lim_{r\to 1^-}\frac{\int_r^1\omega(s)\,ds}{\omega(r)(1-r)}=\infty.$ Every such $A^p_\omega$ lies between the Hardy space $H^p$ and every classical weighted Bergman space $A^p_\alpha$. Even if it is well known that $H^p$ is the limit of $A^p_\alpha$, as $\alpha\to-1$, in many respects, it is shown that $A^p_\omega$ lies ``closer'' to $H^p$ than any $A^p_\alpha$, and that several finer function-theoretic properties of $A^p_\alpha$ do not carry over to $A^p_\omega$.
Function Classes on the Unit Disc
Author: Miroslav Pavlović
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2019-08-19
This revised and extended edition of a well-established monograph in function theory contains a study on various function classes on the disc, a number of new results and new or easy proofs of old but interesting theorems (for example, the Fefferman–Stein theorem on subharmonic behavior or the theorem on conjugate functions in Bergman spaces) and a full discussion on g-functions.