Weighted Bergman spaces induced by rapidly increasing weights

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...

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Bibliographic Details
Main Author: Pelaez, Jose Angel
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2013
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Bergman spaces
Functions of several complex variables
Integral operators
Bergman space
linear differential equation
regular weight
oscillation of solutions
Carleson measure
normal weight
integral operator
factorization
maximal function
Bekollé-Bonami weight
zero set
zero distribution
growth of solutions
rapidly increasing weight
Hardy space
Schatten class
ISBN:0821888021, 9780821888025
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Summary: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 $A^p_\omega$.
Bibliography:Bibliography: p. 119-122
Volume 227, number 1066 (second of 4 numbers), January 2014
Includes index
ISBN:0821888021
9780821888025
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1066