Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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PARAMETER MARCINKIEWICZ INTEGRAL AND ITS COMMUTATOR ON GENERALIZED ORLICZ-MORREY SPACES

  • Lu, Guanghui (College of Mathematics and Statistics Northwest Normal University)
  • Received : 2020.02.11
  • Accepted : 2020.06.04
  • Published : 2021.03.01
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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

Acknowledgement

This work was financially supported by the Innovation Capacity Improvement Project for Colleges and Universities of Gansu Province (No. 2020A-010) and the Doctoral Scientific Research Foundation of Northwest Normal University (No. 6014/0002020203).

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