Weighted Bergman spaces induced by rapidly increasing weights / Jose Angel Pelaez and Jouni Rattya.

"January 2014, volume 227, number 1066 (second of 4 numbers)."

Includes bibliographical references (pages 119-122) and index.

1. Basic notation and introduction to weights --
2. Description of q-Carleson measures for APw --
3. Factorization and zeros of functions in APw --
4. Integral operators and equivalent norms --
5. Non-conformally invariant space induced by Tg on APw --
6. Schatten classes of the inregral operator Tg on A2w --
7. Applications to differential equations --
8. Further discussion--
Bibliography--
Index.

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 $A^p_\omega$.