Maximal and singular integral operators and their commutators in variable exponent generalized weighted Morrey spaces

We consider the generalized weighted Morrey spaces Mp(·),φ ω (R n) with variable exponent p(x) and a general function φ(x, r) defining the Morrey- type norm. 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 max- imal operator and Calderon-Zygmund singular operators in the variable exponent generalized weighted Morrey spaces.