GENERALIZED HOLDER TYPE SPACES OF HARMONIC FUNCTIONS IN THE UNIT BALL AND HALF SPACE

摘要

We study spaces of Holder type functions harmonic in the unit ball and half space with some smoothness conditions up to the boundary. The first type is the Holder type space of harmonic functions with prescribed modulus of continuity omega=omega(h) and the second is the variable exponent harmonic Holder space with the continuity modulus |h|(lambda(center dot)). We give a characterization of functions in these spaces in terms of the behavior of their derivatives near the boundary.