Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (5): 892-903.

• Articles • Previous Articles     Next Articles

Weighted Endpoint Estimates for Multilinear Commutators of Marcinkiewicz Integrals

 ZHANG Pu1, WU Jiang-Long1, LIU Qiang-Guo2   

  1. 1.Department of Mathematics, Mudanjiang Normal University, Heilongjiang Mudanjiang 157011|2.Laboratory for Multiphase Processes, University of Nova Gorica, Nova Gorica 5000, Slovenia
  • Received:2010-10-08 Revised:2012-04-06 Online:2012-10-25 Published:2012-10-25
  • Supported by:

    黑龙江省自然科学基金(A200913)资助

Abstract:

Let μΩ,b be the multilinear commutator generalized by μΩ, the n-dimensional Marcinkiewicz integral, and bj∈BMO(Rn)(1≤j ≤m). The authors establish the weighted weak L(log L)m -type estimates for μΩ,b when Ω satisfies a kind of Dini conditions.

Key words: Marcinkiewicz integral, Multilinear commutator, BMO(Rn),  Ap weight

CLC Number: 

  • 42B20
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