Weighted Bergman Spaces Induced by Rapidly Increasing Weights
Share this pageJosé 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