A New Approach to Function Spaces on Quasi-Metric Spaces

Abstract

A d-space X = (X, , µ) is a compact set X with respect to a quasi-metric and a Borel measure µ such that the measure of a ball of radius r is equivalent to rd , where d > 0. The paper deals with spaces Bp (X ; H ) of Besov type where s 1 < p < and s R. Here H is a bi-Lipschitzian map of the snowflaked version (X, , µ) of X for some 0 < < 1, onto a fractal d/-set = H X in s/ some Rn , reducing the spaces Bp (X ; H ) to the better known spaces Bp (). s