ON THE BOUNDARY BEHAVIOR OF FUNCTIONS IN SPACES OF HARDY TYPE

Abstract

Let be a topological space with a measure . In the product (or ) simple axioms are used to distinguish a family of domains for approaching the boundary of . Associated with the family is the maximal function The spaces consisting of functions continuous on with are introduced, along with the subspaces of them consisting of the functions having a -limit a.e. The properties of the spaces and the action in them of operators of smoothing type are studied. The results are applied to Hardy spaces of harmonic or holomorphic functions.