GENERALIZED WEIGHTED HARDY OPERATORS AND THEIR COMMUTATORS IN THE LOCAL ”COMPLEMENTARY” GENERALIZED VARIABLE EXPONENT WEIGHTED MORREY SPACES

Abstract

In this paper we study the boundedness of weighted Hardy operators Hα u and Hα u in local ”complementary” generalized variable exponent weighted Morrey spaces {M p(·),ω,ϕ {0} , characterized by variable exponent p(x), a general function ω(r) and a weight ϕ. We also study the boundedness of the commutators of Hα u and Hα u in the spaces {M p(·),ω,ϕ {0} .