On inner functions with derivative in Bergman spaces (Q1090805)

Let \(A^{p,\alpha}\) be the weighted Bergman space of functions holomorphic in the unit disc and \(\Phi\) an inner function. For \(1\leq p\leq 2\), \(\alpha >-1\), \textit{P. Ahern} [Indiana Univ. Math. J. 28, 311-347 (1979; Zbl 0415.30022)] described a necessary and sufficient condition for \(\phi '\in A^{p,\alpha}\). The purpose of this paper is to extend these to \(1\leq p<\infty.\) The author mentions that \textit{I. Eh. Verbitskij} announced a generalization of the results of \textit{P. Ahern} without supplying proofs. These proofs may be found in Sib. Mat. Zh. 26, No.2(150), 51-72 (1985; Zbl 0591.46025).