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

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