Abstract
In this paper, we establish the weighted sharp maximal function inequalities for the multilinear singular integral operators. As an application, we obtain the boundedness of the multilinear operators on weighted Lebesgue and Morrey spaces. MSC:42B20, 42B25.
Highlights
As the development of singular integral operators, their commutators operators have been well studied
In [ – ], the authors prove that the commutators generated by the singular integral operators and BMO functions are bounded on Lp(Rn) for < p < ∞
In [, ], the boundedness for the commutators generated by the singular integral operators and Lipschitz functions on Triebel-Lizorkin and Lp(Rn) ( < p < ∞) spaces are obtained
Summary
As the development of singular integral operators (see [ – ]), their commutators operators have been well studied. In [ , ], the boundedness for the commutators generated by the singular integral operators and the weighted BMO and Lipschitz functions on Lp(Rn) ( < p < ∞) spaces are obtained ( see [ , ]). We will study the multilinear operator generated by the singular integral operator and the weighted Lipschitz and BMO functions, that is, Dαb ∈ BMO(w) or Dαb ∈ Lipβ (w) for all α with |α| = m. The main purpose of this paper is to prove the sharp maximal inequalities for the multilinear operator Tb. As the application, we obtain the weighted Lp-norm inequality and Morrey space boundedness for the multilinear operator Tb. r < ∞, < β < and Dαb ∈ Lipβ (w) for all α with |α| = m.
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