Convolution and potential type operators in Lp(x) (Rn )

Abstract

In this paper we give a further development of the results of the paper [1] and apply it to convolution operators in the spaces Lp(x) . We consider the question of extendability of the Young theorem: well known for constant p and q, to the case when they may be variable. We also potential type operators with the Kernel . In section 1 we develop some estimates for Lp(x) -norms of power functions of distance truncated to exterior of a ball of radius . Section 2 deals with convolution operators in the spaces Lp(x) and Section 3 is devoted to potential type operators.