Vol. 57, No. 2, 1975

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Behavior of Φ-bounded harmonic functions at the Wiener boundary

Young K. Kwon

Vol. 57 (1975), No. 2, 453–455
Abstract

For a strongly convex Φ(t), denote by HΦ the class of Φ-bounded harmonic functions, and by CΦ the class of continuous functions f on the Wiener harmonic boundary such that the composite Φ(|f|) is integrable with respect to a harmonic measure. Theorem: u HΦ if and only if u is a solution of the Dirichlet problem with boundary values f CΦ on the Wiener harmonic boundary.

Mathematical Subject Classification 2000
Primary: 31C05
Milestones
Received: 13 February 1975
Revised: 18 March 1975
Published: 1 April 1975
Authors
Young K. Kwon