Frontiers of Mathematics in China >

2017 , Vol. 12 >Issue 3: 531 - 558

DOI: https://doi.org/10.1007/s11464-017-0634-3

RESEARCH ARTICLE

Multiple weighted estimates for maximal vector-valued commutator of multilinear Calderón-Zygmund singular integrals

  • Dongxiang CHEN , 1 ,
  • Shanzhen LU 2 ,
  • Suzhen MAO 1
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  • 1. Department of Mathematics, Jiangxi Normal University, Nanchang 330022, China
  • 2. School of Mathematical Science, Beijing Normal University, Beijing 100875, China

Received date: 23 Sep 2012

Accepted date: 12 Dec 2016

Published date: 20 Apr 2017

Copyright

2017 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular integrals operator is obtained. On the other hand, pointwise estimates for sharp maximal function of two kinds of maximal vector-valued multilinear singular integrals and maximal vector-valued commutators are also established. By the weighted estimates of a class of new variant maximal operator, Cotlar’s inequality and the sharp maximal function estimates, multiple weighted strong estimates and weak estimates for maximal vector-valued singular integrals of multilinear operators and those for maximal vector-valued commutator of multilinear singular integrals are obtained.

Key words： Multilinear singular integrals; vector-valued commutator; multiple weight; maximal functions

Cite this article

Dongxiang CHEN , Shanzhen LU , Suzhen MAO . Multiple weighted estimates for maximal vector-valued commutator of multilinear Calderón-Zygmund singular integrals[J]. Frontiers of Mathematics in China, 2017 , 12(3) : 531 -558 . DOI: 10.1007/s11464-017-0634-3

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