Memoirs of the American Mathematical Society 2014; 124 pp; softcover Volume: 227 ISBN10: 0821888021 ISBN13: 9780821888025 List Price: US$77 Individual Members: US$46.20 Institutional Members: US$61.60 Order Code: MEMO/227/1066
 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 \(\lim_{r\to 1^}\frac{\int_r^1\omega(s)\,ds}{\omega(r)(1r)}=\infty.\) 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 \(\alpha\to1\), in many respects, it is shown that \(A^p_\omega\) lies "closer" to \(H^p\) than any \(A^p_\alpha\), and that several finer functiontheoretic properties of \(A^p_\alpha\) do not carry over to \(A^p_\omega\). Table of Contents  Preface
 Basic notation and introduction to weights
 Description of \(q\)Carleson measures for \(A^p_\omega\)
 Factorization and zeros of functions in \(A^p_\omega\)
 Integral Operators and equivalent norms
 Nonconformally invariant space induced by \(T_g\) on \(A^p_\omega\)
 Schatten classes of the integral operator \(T_g\) on \(A^2_\omega\)
 Applications to differential equations
 Further discussion
 Bibliography
 Index
