The boundary modulus of continuity of harmonic functions

Elgin Johnston
1980 Pacific Journal of Mathematics  
Let G be a bounded domain in the complex plane and let u(z) be continuous on G. In this paper we study the boundary modules of continuity, ω(δ), of u on dG and the modulus of continuity, ω(δ), of u on G. We investigate the extent to which the inequality "ω(δ) <ω(<5)" holds when u is harmonic on G and show that the precise formulation of such inequalities depends on the smoothness of dG.
doi:10.2140/pjm.1980.90.87 fatcat:mopba66cgjf4hfsca76jvypogy