J. Korean Math. Soc. 2021; 58(2): 383-400
Online first article July 31, 2020 Printed March 1, 2021
https://doi.org/10.4134/JKMS.j200071
Copyright © The Korean Mathematical Society.
Guanghui Lu
Northwest Normal University
The aim of this paper is to mainly establish the sufficient and necessary conditions for the boundedness of the commutator $\mathcal{M}^{\rho}_{\Omega, b}$ which is generated by the parameter Marcinkiwicz integral $\mathcal{M}^{\rho}_{\Omega}$ and the Lipschitz function $b$ on generalized Orlicz-Morrey space $L^{\Phi,\varphi}(\mathbb{R}^{d})$ in the sense of the Adams type result (or Spanne type result). Moreover, the necessary conditions for the parameter Marcinkiewizcz integral $\mathcal{M}^{\rho}_{\Omega}$ on the $L^{\Phi,\varphi}(\mathbb{R}^{d})$, and the commutator $[b,\mathcal{M}^{\rho}_{\Omega}]$ generated by the $\mathcal{M}^{\rho}_{\Omega}$ and the space $\mathrm{BMO}$ on the $L^{\Phi,\varphi}(\mathbb{R}^{d})$, are also obtained, respectively.
Keywords: Parameter Marcinkiewicz integral, commutator, Lipschits space, $\mathrm{BMO}$ space, generalized Orlicz-Morrey
MSC numbers: Primary 42B20, 42B35
Supported by: 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)
2022; 59(2): 235-254
2018; 55(4): 939-962
2018; 55(3): 671-694
2017; 54(3): 713-732
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd