Singular and fractional integral operators on Campanato spaces with variable growth conditions

Abstract

Let X be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we prove boundedness of singular and fractional integral operators on Campanato spaces over X with variable growth conditions. The function spaces contain generalized Lipschitz spaces with variable exponent as special cases. Moreover, by using the function spaces, we can deal with functions which are Lp-functions locally on one subset in X, BMO-functions locally on one another subset and Lipα-functions locally on the other one. Our results are new even for ℝn case.