Convolution and potential type operators in L^p(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 L^p(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 L^p(x) -norms of power functions of distance truncated to exterior of a ball of radius . Section 2 deals with convolution operators in the spaces L^p(x) and Section 3 is devoted to potential type operators.

Keywords:

• potential theory
• convolution operators
• singular integrals

MSC(1991):

• 31B10
• 42B20
• 44A35
• 47B38