Vol. 90, No. 1, 1980

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The boundary modulus of continuity of harmonic functions

Elgin Harold Johnston

Vol. 90 (1980), No. 1, 87–98
Abstract

Let G be a bounded domain in the complex plane and let u(z) be continuous on . In this paper we study the boundary modules of continuity, ω(δ), of u on ∂G and the modulus of continuity, ω(δ), of u on . We investigate the extent to which the inequality “ω(δ) ω(δ)” holds when u is harmonic on G and show that the precise formulation of such inequalities depends on the smoothness of ∂G.

Mathematical Subject Classification 2000
Primary: 31A05
Secondary: 30A10
Milestones
Received: 2 June 1978
Published: 1 September 1980
Authors
Elgin Harold Johnston