Maximal and singular integral operators and their commutators on generalized weighted morrey spaces with variable exponent

We consider the generalized weighted Morrey spaces Mp(),σ w (Ω) with variable exponent p(x) and a general function σ(x, r) defining the Morrey-type norm. In case of unbounded sets Ω ⊂ Rn we prove the boundedness of the Hardy-Littlewood maximal operator and Calderón-Zygmund singular operators with standard kernel, in such spaces. We also prove the boundedness of the commutators of maximal operator and Calderón-Zygmund singular operators in the generalized weighted Morrey spaces with variable exponent. © ELEMEN , Zagreb.