| eBook ISBN: | 978-1-4704-1427-6 |
| Product Code: | MEMO/227/1066.E |
| List Price: | $77.00 |
| MAA Member Price: | $69.30 |
| AMS Member Price: | $46.20 |
| eBook ISBN: | 978-1-4704-1427-6 |
| Product Code: | MEMO/227/1066.E |
| List Price: | $77.00 |
| MAA Member Price: | $69.30 |
| AMS Member Price: | $46.20 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 227; 2014; 124 ppMSC: Primary 30; Secondary 47
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 \(A^p_\omega\).
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Table of Contents
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Chapters
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Preface
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1. Basic Notation and Introduction to Weights
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2. Description of $q$-Carleson Measures for $A^p_\omega $
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3. Factorization and Zeros of Functions in $A^p_\omega $
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4. Integral Operators and Equivalent Norms
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5. Non-conformally Invariant Space Induced by $T_g$ on $A^p_\omega $
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6. Schatten Classes of the Integral Operator $T_g$ on $A^2_\omega $
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7. Applications to Differential Equations
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8. Further Discussion
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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 \(A^p_\omega\).
-
Chapters
-
Preface
-
1. Basic Notation and Introduction to Weights
-
2. Description of $q$-Carleson Measures for $A^p_\omega $
-
3. Factorization and Zeros of Functions in $A^p_\omega $
-
4. Integral Operators and Equivalent Norms
-
5. Non-conformally Invariant Space Induced by $T_g$ on $A^p_\omega $
-
6. Schatten Classes of the Integral Operator $T_g$ on $A^2_\omega $
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7. Applications to Differential Equations
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8. Further Discussion
