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On a Representation of the Derivative of a Conformal Mapping
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G. Khuskivadze
Published/Copyright:
February 24, 2010
Abstract
Let ω conformally map the unit circle on a plane singly-connected domain D bounded by a simple rectifiable curve. It is shown that for the function lg ω′ to be represented in the unit circle by a Cauchy type A-integral with density arg ω′, it is necessary and sufficient that D be a Smirnov domain. In particular, for this representation to be done by a Cauchy–Lebesgue type integral with the same density, it is necessary and sufficient that the function lg ω′ belong to the Hardy class H1.
Key words and phrases:: Conformal mapping; Smirnov domain; extension of Lebesgue integral; A-integral
Received: 2001-03-26
Published Online: 2010-02-24
Published in Print: 2001-September
© Heldermann Verlag
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Keywords for this article
Conformal mapping;
Smirnov domain;
extension of Lebesgue integral;
A-integral
Articles in the same Issue
- A New Method of Solving the Basic Plane Boundary Value Problems of Statics of the Elastic Mixture Theory
- Euler Polynomials and the Related Quadrature Rule
- MD-Numbers and Asymptotic MD-Numbers of Operators
- Boundary Variational Inequality Approach in the Anisotropic Elasticity for the Signorini Problem
- On Vector Sums of Measure Zero Sets
- Hyper-Holomorphic Cells and Fredholm Theory
- On a Representation of the Derivative of a Conformal Mapping
- On a Trace Inequality for One-Sided Potentials and Applications to the Solvability of Nonlinear Integral Equations
- Quasiconformal Deformations of Holomorphic Functions
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- Pluriregular, Plurigeneralized Regular Equations in Clifford Analysis
- On Volterra Type Singular Integral Equations
