On commutators of vector BMO functions and multilinear singular integrals with non-smooth kernels

Bui The Anh*, Xuan Thinh Duong

*Corresponding author for this work

Research output: Contribution to journalArticle

15 Citations (Scopus)

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 b and T is bounded on certain product Lp(Rn) spaces. We obtain boundedness of the commutator of b 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.

Original languageEnglish
Pages (from-to)80-94
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Volume371
Issue number1
DOIs
Publication statusPublished - Nov 2010

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