Weighted Bergman spaces induced by rapidly increasing weights
Author(s)
Bibliographic Information
Weighted Bergman spaces induced by rapidly increasing weights
（Memoirs of the American Mathematical Society, no. 1066）
American Mathematical Society, c2013
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Note
"Volume 227, number 1066 (second of 4 numbers), January 2014"
Bibliography: p. 119-122
Includes index
Description and Table of Contents
Description
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 $A^p_\omega$.
by "Nielsen BookData"
