Maximal and singular operators in the local "complementary" generalized variable exponent Morrey spaces on unbounded sets

Abstract

In this paper we consider local “complementary” generalized Morrey spaces  with variable exponent p(x) and a general function ω(r) defining a Morrey-type norm. We prove the boundedness of the Hardy-Littlewood maximal operator and Calderón-Zygmund singular operators with standard kernel in such spaces in case of unbounded sets Ω ⊂ ℝ ⁿ . Also we prove the  boundedness of commutators of Hardy-Littlewood maximal operator and Calderón-Zygmund singular integral operators.