Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (2): 320-335.

• Articles • Previous Articles     Next Articles

Endpoint Estimates for Higher Order Maximal Commutators

 QIAO Dan, YANG Mei-Jin, CHEN Jian-Ren   

  1. School of Mathematical Sciences, Harbin Normal University, Harbin 150025
  • Received:2010-09-22 Revised:2011-11-18 Online:2012-04-25 Published:2012-04-25
  • Supported by:

    国家自然科学基金(11071052)和哈尔滨师范大学博士项目资助

Abstract:

In this paper, the authors establish that higher order maximal commutators of singular integral operator Tb, m* satisfy the following inequality
|{yRn:Tb, m*f(y)>λ}|≤C||b||mBMORn|f(y)|/λ (1+log+|f(y)|/λ)mdy
and are bounded on Lp(Rn), 1 < p <∞, when b is a
BMO function.

Key words: Higher order maximal commutators, Singular integral operator, Doubling Young function

CLC Number: 

  • 42B20
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