Boundedness of Marcinkiewicz Integrals and Their Commutators on Generalized Weighted Morrey Spaces

Abstract

We will study the boundedness of Marcinkiewicz integrals with rough kernel on the generalized weighted Morrey spaces. We will also prove that the commutator operators formed by aBMORnfunction and Marcinkiewicz integrals are also bounded on the generalized weighted Morrey spaces.

Commutators of parametric Marcinkiewicz integrals on generalized Orlicz-Morrey spaces

“…The proof follows from the Lemmas 5 and 7. We can also give the following alternative proof for Theorem 1 by inspiring the ideas in [4]. Since f 2 M ;' 1 (R n ) and ' 1 ; ' 2 and satisfy the condition (3.7), we have…”