On the boundedness of the maximal operator and singular integral operators in generalized morrey spaces

Abstract

In the paper we find conditions on the pair (? 1, ? 2) which ensure the boundedness of the maximal operator and the Calderón-Zygmund singular integral operators from one generalized Morrey space M p,?1 to another M p,?2, 1 < p < ?, and from the space M 1,?1 to the weak space W M1,?2. As applications, we get some estimates for uniformly elliptic operators on generalized Morrey spaces.