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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.
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참고문헌 (32)
참고문헌 신청
H. Al-Qassem / 2002 / Lp bounds for the function of Marcinkiewicz / Mathematical Research Letters 9(5):697~700
A. P. Calderon / 1965 / COMMUTATORS OF SINGULAR INTEGRAL OPERATORS / Proceedings of the National Academy of Sciences 53(5):1092~1099
Yanping Chen / 2015 / Lp boundedness of the commutators of Marcinkiewicz integrals with rough kernels / Forum Mathematicum 27(4):2087~2111
Yan Ping Chen / 2011 / Commutators of Marcinkiewicz integral with rough kernels on Sobolev spaces / Acta Mathematica Sinica, English Series 27(7):1345~1366
R. R. Coifman / 1976 / Factorization Theorems for Hardy Spaces in Several Variables / The Annals of Mathematics 103(3):611
A. P. Calderon / 1965 / COMMUTATORS OF SINGULAR INTEGRAL OPERATORS / Proceedings of the National Academy of Sciences 53(5):1092~1099
Yanping Chen / 2015 / Lp boundedness of the commutators of Marcinkiewicz integrals with rough kernels / Forum Mathematicum 27(4):2087~2111
Yan Ping Chen / 2011 / Commutators of Marcinkiewicz integral with rough kernels on Sobolev spaces / Acta Mathematica Sinica, English Series 27(7):1345~1366
R. R. Coifman / 1976 / Factorization Theorems for Hardy Spaces in Several Variables / The Annals of Mathematics 103(3):611
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