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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| Format: | E-Book Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
2013
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| Ausgabe: | 1 |
| Schriftenreihe: | Memoirs of the American Mathematical Society |
| Schlagworte: | |
| ISBN: | 0821888021, 9780821888025 |
| ISSN: | 0065-9266, 1947-6221 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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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| Bibliographie: | 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 |