PARAMETER MARCINKIEWICZ INTEGRAL AND ITS COMMUTATOR ON GENERALIZED ORLICZ-MORREY SPACES

Abstract

The aim of this paper is to mainly establish the sufficient and necessary conditions for the boundedness of the commutator ����Ω,b which is generated by the parameter Marcinkiwicz integral ����Ω and the Lipschitz function b on generalized Orlicz-Morrey space L��,��(Rd) in the sense of the Adams type result (or Spanne type result). Moreover, the necessary conditions for the parameter Marcinkiewizcz integral ����Ω on the L��,��(Rd), and the commutator [b,����Ω] generated by the ����Ω and the space BMO on the L��,��(Rd), are also obtained, respectively.

Keywords

• Parameter Marcinkiewicz integral;
• commutator;
• Lipschits space;
• BMO space;
• generalized Orlicz-Morrey

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