IJPAM: Volume 75, No. 4 (2012)

THE RIEMANN BOUNDARY VALUE PROBLEM FOR
$\b$-ANALYTIC FUNCTIONS OVER $D$-SUMMABLE
CLOSED CURVES

Ricardo Abreu-Blaya$^1$, Juan Bory-Reyes$^2$, Jean-Marie Vilaire$^3$
$^1$Facultad de Informática y Matemática
Universidad de Holguın
Holguın 80100, CUBA
$^2$Departamento de Matemática
Universidad de Oriente
Santiago de Cuba, 90500, CUBA
$^3$Departamento de Matemáticas
Universidad Carlos III de Madrid
Leganés 28911, Madrid, SPAIN


Abstract. The aim of this paper is to describe solvability conditions of the $\b$-analytic Riemann boundary value problem in a Jordan domain of the complex plane whose boundary is assumed to be a summable closed curve.

Received: October 14, 2011

AMS Subject Classification: 30G35

Key Words and Phrases: $\b$-analytic functions, Riemann boundary value problem, fractal dimensions

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 75
Issue: 4