**Memoirs of the American Mathematical Society**

2014;
124 pp;
Softcover

MSC: Primary 30;
Secondary 47

Print ISBN: 978-0-8218-8802-5

Product Code: MEMO/227/1066

List Price: $77.00

AMS Member Price: $46.20

MAA Member Price: $69.30

**Electronic ISBN: 978-1-4704-1427-6
Product Code: MEMO/227/1066.E**

List Price: $77.00

AMS Member Price: $46.20

MAA Member Price: $69.30

# Weighted Bergman Spaces Induced by Rapidly Increasing Weights

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*José Ángel Peláez; Jouni Rättyä*

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 \(A^p_\omega\).

#### Table of Contents

# Table of Contents

## Weighted Bergman Spaces Induced by Rapidly Increasing Weights

- Preface 18 free
- Chapter 1. Basic Notation and Introduction to Weights 512 free
- Chapter 2. Description of 𝑞-Carleson Measures for 𝐴^{𝑝}_{\om} 1926
- Chapter 3. Factorization and Zeros of Functions in 𝐴^{𝑝}_{\om} 2936
- Chapter 4. Integral Operators and Equivalent Norms 4956
- Chapter 5. Non-conformally Invariant Space Induced by 𝑇_{𝑔} on 𝐴^{𝑝}_{\om} 7178
- Chapter 6. Schatten Classes of the Integral Operator 𝑇_{𝑔} on 𝐴²_{\om} 8390
- Chapter 7. Applications to Differential Equations 101108
- Chapter 8. Further Discussion 115122
- Bibliography 119126
- Index 123130 free