On commutators of vector BMO functions and multilinear singular integrals with non-smooth kernels |
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Authors: | Bui The Anh Xuan Thinh Duong |
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Institution: | a Department of Mathematics, Macquarie University, NSW 2109, Australia b Department of Mathematics, University of Pedagogy, Ho chi Minh city, Viet Nam |
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Abstract: | Let T be a bounded multilinear operator on some product of Lq(Rn) spaces. Assume that T has a non-smooth associated kernel which satisfies certain weak regularity conditions but not regular enough to fall under the scope of the standard multilinear Calderón-Zygmund theory. The main aim of this paper is to establish a sufficient condition on the kernel of T so that the commutator of a vector BMO function and T is bounded on certain product Lp(Rn) spaces. We obtain boundedness of the commutator of and T by first proving certain pointwise estimates on the Fefferman-Stein sharp maximal operator. An important example of multilinear operators which satisfy our kernel conditions is the maximal mth order Calderón commutator. |
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Keywords: | Multilinear singular integrals Maximal singular integrals Weighted norm inequalities Generalized Calderó n-Zygmund operator Commutators |
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