Kim, Hong Oh Derivatives of Blaschke products. (English) Zbl 0551.30029 Pac. J. Math. 114, 175-190 (1984). This paper is a study of the behavior of the derivative of an infinite Blaschke product, focusing on membership of the derivative B’ or fractional derivatives \(B^{\beta}\) in the classes \(A^{p,\alpha}\). Here \(A^{p,\alpha}\) \((0<p<\infty,\quad \alpha >-1)\) is the set of all f(z), holomorphic in \(| z| <1,\) and satisfying \[ \int^{1}_{0}\int^{2\pi}_{0}| f(re^{it})|^ p\quad (1- r)^{\alpha}\quad d\theta \quad dr<\infty. \] Some necessary and some sufficient conditions for the above mentioned membership are given, which generalize results of P. Ahern and the reviewer [Mich. Math. J. 21, 115-127 (1974; Zbl 0287.30034)] and P. Ahern [Indiana Univ. Math. J. 28, 311-347 (1979; Zbl 0415.30022)]. The conditions are given in terms of the zeros and occasionally the power series coefficients of B. Reviewer: D.N.Clark Cited in 1 ReviewCited in 26 Documents MSC: 30D50 Blaschke products, etc. (MSC2000) 30B10 Power series (including lacunary series) in one complex variable 30D55 \(H^p\)-classes (MSC2000) 26A33 Fractional derivatives and integrals 30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) Keywords:extensions of Hardy-Littlewood theorem; fractional integrals; embedding theorem; infinite Blaschke product; fractional derivatives Citations:Zbl 0287.30034; Zbl 0415.30022 PDFBibTeX XMLCite \textit{H. O. Kim}, Pac. J. Math. 114, 175--190 (1984; Zbl 0551.30029) Full Text: DOI