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

We consider the vanishing generalized weighted Morrey spaces V Mp(·),ϕ ω (Ω) with variable exponent p(x) and a general function ϕ(x, r) defining the Morrey-type norm. In case of unbounded sets Ω ⊂ 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 vanishing generalized ´ weighted Morrey spaces with variable exponent.