Integral Means of the Logarithmic Derivative of Blaschke Products

被引：0

作者：

Javad Mashreghi

Mahmood Shabankhah

机构：

[1] Université Laval,

来源：

Computational Methods and Function Theory | 2009年 / 9卷 / 2期

关键词：

Blaschke products; integral means; Hardy spaces; Bergman spaces; Primary 30D50; Secondary 26A12;

D O I：

10.1007/BF03321737

中图分类号：

学科分类号：

摘要：

Let B be a Blaschke product for the open unit disc with zeros (zn)n>1. We assume that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sum_{n=1}^{\infty}h(1-|z_n|)<\infty$\end{document}, where h is a given positive continuous functions. A typical example that has been extensively studied before is h(t) = tα, 0 < α < 1. Then we find upper bounds for the Hardy and Bergman means of the logarithmic derivative of B.

引用

页码：421 / 433

页数：12

共 19 条

[1]

Ahern P R(1974)On inner functions with H Michigan Math. J 21 115-127

[2]

Clark D N(1976)-derivative Michigan Math. J 23 107-118

[3]

Ahern P R(2003)On inner functions with B Proc. London Math. Soc. (3) 86 735-754

[4]

Clark D N(1983)-derivative Michigan Math. J 30 221-229

[5]

Chyzhykov I(2007)Linear differential equations and logarithmic derivative estimates Kodai Math. J 30 147-155

[6]

Gundersen G(1988)On the H J. London Math. Soc (2) 37 88-104

[7]

Heittokangas J(1998) classes of derivative of functions orthogonal to invariant subspaces Trans. Amer. Math. Soc 350 1225-1247

[8]

Cohn W S(2007)On integral means of the derivatives of Blaschke products Kodai Math. J 30 263-279

[9]

Gotoh Y(2002)Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates Kodai Math. J 25 191-208

[10]

Gundersen G(1976)The possible orders of solutions of linear differential equations with polynomial coefficients Michigan Math. J 23 43-51

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