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

Abstract

Abstract. We consider the generalized weighted Morrey spaces M p(·),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 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 Mathematics subject classification (2010): 42B20, 42B25, 42B35.

Commutators of Riesz potential in the vanishing generalized weighted Morrey spaces with variable exponent

“…The variable exponent generalized weighted Morrey spaces M p(·),ϕ ω (Ω) over an open set Ω ⊂ R n was introduced and the boundedness of the Hardy-Littlewood maximal operator, the singular integral operators and their commutators on these spaces was proven in [28]. The main focus of this article is to prove that the Riesz potential and its commutators are bounded on generalized weighted Morrey spaces M (Ω) are proved.…”

“…[28] Let Ω ⊂ R n be an open unbounded set, p ∈ P log ∞ (Ω) , ω ∈ A p(·) (Ω) , b ∈ BMO(Ω) and the function ϕ 1 (x, r) and ϕ 2 (x, r) satisfy the condition…”