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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Hlavný autor:	Pelaez, Jose Angel
Médium:	E-kniha Kniha
Jazyk:	English
Vydavateľské údaje:	Providence, Rhode Island American Mathematical Society 2013
Vydanie:	1
Edícia:	Memoirs of the American Mathematical Society
Predmet:	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
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Shrnutí:	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 $A^p_\omega$.
Bibliografia:	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