MAXIMAL AND SINGULAR INTEGRAL OPERATORS AND THEIR COMMUTATORS ON GENERALIZED WEIGHTED MORREY SPACES WITH VARIABLE EXPONENT

Abstract

We consider the generalized weighted Morrey spaces M-omega(p(.),phi) (Omega) with variable exponent p(x) and a general function phi(x, r) defining the Morrey-type norm. In case of unbounded sets Omega subset of R-n we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove the boundedness of the commutators of maximal operator and Calderon-Zygmund singular operators in the generalized weighted Morrey spaces with variable exponent