Logarithmic convexity of area integral means for analytic functions

Chunjie Wang; Kehe Zhu

doi:10.7146/math.scand.a-16643

Logarithmic convexity of area integral means for analytic functions

Chunjie Wang
, Kehe Zhu

Mathematics and Statistics

University at Albany

Hebei University of Technology

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We show that the L² integral mean on rD of an analytic function in the unit disk D with respect to the weighted area measure (1 - |z|2) ^α dA(z), where -3 ≤ α ≤ 0, is a logarithmically convex function of r on (0, 1).We also show that the range [-3, 0] for ≤ is best possible.

Original language	English
Pages (from-to)	149-160
Number of pages	12
Journal	Mathematica Scandinavica
Volume	114
Issue number	1
DOIs	https://doi.org/10.7146/math.scand.a-16643
State	Published - 2014

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abstract = "We show that the L2 integral mean on rD of an analytic function in the unit disk D with respect to the weighted area measure (1 - |z|2) α dA(z), where -3 ≤ α ≤ 0, is a logarithmically convex function of r on (0, 1).We also show that the range [-3, 0] for ≤ is best possible.",

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AU - Zhu, Kehe

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AB - We show that the L2 integral mean on rD of an analytic function in the unit disk D with respect to the weighted area measure (1 - |z|2) α dA(z), where -3 ≤ α ≤ 0, is a logarithmically convex function of r on (0, 1).We also show that the range [-3, 0] for ≤ is best possible.

UR - https://www.scopus.com/pages/publications/84901629158

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DO - 10.7146/math.scand.a-16643

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VL - 114

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EP - 160

JO - Mathematica Scandinavica

JF - Mathematica Scandinavica

IS - 1

ER -

Logarithmic convexity of area integral means for analytic functions

Abstract

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