Acta mathematica scientia,Series A ›› 2015, Vol. 35 ›› Issue (6): 1106-1114.

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Necessary and Sufficient Conditions for Boundedness of Commutators of Multilinear Fractional Integral Operators

Wang Songbai1, Pan Jibing1, Jiang Yinsheng2   

  1. 1 College of Mathematics and statistics, Hubei Normal University, Huangshi 435002;
    2 College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046
  • Received:2015-04-16 Revised:2015-10-11 Online:2015-12-25 Published:2015-12-25

Abstract:

Let ωA1, 0<α<mn and 0<β<1 such that α+β<mn, and let 1<p1,…,pm<∞ with 1/q=1/p-(α+β)/n>0 and 1/p=1/p1+…+1/pm. We obtain that b∈Lipβ(ω)m if and only if the commutators[Σb,Iα] generated by multilinear fractional integral operators Iα and the symbols b are bounded from Lp1(ω)× …× Lpm(ω) to Lq(ω1-(1-α/n)q).

Key words: Multilinear fractional integral operator, Lipβ spaces, Commutators

CLC Number: 

  • O174.2
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