Integral operators on local Orlicz-Morrey spaces

Abstract

We establish a general principle on the boundedness of operators on local Orlicz-Morrey spaces. As applications of this principle, we obtain the boundedness of the Calder?n-Zygmund operators, the nonlinear commutators of the Calder?n-Zygmund operators, the oscillatory singular integral operators, the singular integral operators with rough kernels and the Marcinkiewicz integrals on the local Orlicz-Morrey spaces.

Two-weighted inequalities for maximal commutators in generalized weighted Morrey spaces on spaces of homogeneous type

“…For example, M b is a positive and sublinear operator, but [M, b] is neither positive nor sublinear. However, if b satisfies some additional conditions, then operator M b controls [M, b].The maximal operators and their commutators were widely investigated in various Morrey-type spaces (see, for example,[2,5,6,13,36,40,41]).…”