Modulus of continuity of normal derivative of a harmonic functions at a boundary point
Miloš Arsenović, Miodrag Mateljević · Filomat · 2023
We give sufficient conditions which ensure that harmonic extension u = P[f] to the upper half space {(x, y) | x ? Rn, y > 0} of a function f ? Lp(Rn) satisfies estimate ?u/?y (x, y) ? C?(y)/y for every x in E ? Rn, where ? is a majorant. The conditions are expressed in terms of behaviour of the Riesz transforms Rjf of f near points in E. We briefly investigate related questions for the cases of harmonic and hyperbolic harmonic functions in the unit ball.