### Abstract

Let T be a bounded multilinear operator on some product of L^{q}(R^{n}) 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 L^{p}(R^{n}) 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 language | English |
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Pages (from-to) | 80-94 |

Number of pages | 15 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 371 |

Issue number | 1 |

DOIs | |

Publication status | Published - Nov 2010 |