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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Table of Contents:
  • Preface -- Basic Notation and Introduction to Weights -- Description of <inline-formula content-type="math/mathml"> q q </inline-formula>-Carleson Measures for <inline-formula content-type="math/mathml"> A ω p A^p_\omega </inline-formula> -- Factorization and Zeros of Functions in <inline-formula content-type="math/mathml"> A ω p A^p_\omega </inline-formula> -- Integral Operators and Equivalent Norms -- Non-conformally Invariant Space Induced by <inline-formula content-type="math/mathml"> T g T_g </inline-formula> on <inline-formula content-type="math/mathml"> A ω p A^p_\omega </inline-formula> -- Schatten Classes of the Integral Operator <inline-formula content-type="math/mathml"> T g T_g </inline-formula> on <inline-formula content-type="math/mathml"> A ω 2 A^2_\omega </inline-formula> -- Applications to Differential Equations -- Further Discussion
  • Intro -- Contents -- Preface -- Chapter 1. Basic Notation and Introduction to Weights -- 1.1. Basic notation -- 1.2. Regular and rapidly increasing weights -- 1.3. Bekollé-Bonami and invariant weights -- 1.4. Lemmas on weights -- 1.5. Density of polynomials in ^{ }_{ } -- Chapter 2. Description of -Carleson Measures for ^{ }_{\om} -- 2.1. Weighted maximal function _{ } -- 2.2. Proof of the main result -- Chapter 3. Factorization and Zeros of Functions in ^{ }_{\om} -- 3.1. Factorization of functions in ^{ }_{ } -- 3.2. Zeros of functions in ^{ }_{ } -- 3.3. Zeros of functions in the Bergman-Nevanlinna class \mathit{ }_{ } -- Chapter 4. Integral Operators and Equivalent Norms -- 4.1. Equivalent norms on ^{ }_{ } -- 4.2. Integral operator _{ } on the weighted Bergman space ^{ }_{ } -- 4.3. Integral operator _{ } on the Hardy space ^{ } -- Chapter 5. Non-conformally Invariant Space Induced by _{ } on ^{ }_{\om} -- 5.1. Inclusion relations -- 5.2. Structural properties of ¹( ^{⋆}) -- Chapter 6. Schatten Classes of the Integral Operator _{ } on ²_{\om} -- 6.1. Preliminary results -- 6.2. Proofs of the main results -- Chapter 7. Applications to Differential Equations -- 7.1. Solutions in the weighted Bergman space ^{ }_{ } -- 7.2. Solutions in the Bergman-Nevanlinna class \mathit{ }_{ } -- Chapter 8. Further Discussion -- 8.1. Carleson measures -- 8.2. Generalized area operators -- 8.3. Growth and oscillation of solutions -- 8.4. Zero distribution -- Bibliography -- Index