AN APPLICATION OF AN ESTIMATE OF THE RIEMANN MAPPING FUNCTION FOR CERTAIN STAR-SHAPED DOMAINS.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Let D denote a simply connected domain contained in the simply connected star-shaped domain G. Let u denote a harmonic function in G which is bounded by M throughout G and by m , m M, in D. For any compact set S in G, there exist explicitly defined constants K KM,G,D,S and alpha alphaG,D,S, 0 alpha 1, such that the absolute value of u Km to the power alpha throughout S. Author
- Theoretical Mathematics