Acta mathematica scientia, Series B >
WEIGHTED ESTIMATES WITH GENERAL WEIGHTS FOR MULTILINEAR CALDER´|ON-ZYGMUND OPERATORS
Received date: 2010-08-02
Revised date: 2011-04-15
Online published: 2012-07-20
Supported by
The research was supported by the NSFC (10971228).
In this paper, some weighted estimates with general weights are established for the m-linear Calder´on-Zygmund operator and the corresponding maximal operator. It is proved that, if p1, · · · , pm ∈ [1,∞] and p ∈ (0,∞) with 1/p =∑mk=11/pk, then for any weight w, integer l with 1 ≤ l ≤ m, these operators are bounded from Lp1 (Rn, MBw) ×· · ·×Lpl(Rn, MBw)×Lpl+1 (Rn, Mw)×· · ·×Lpm(Rn, Mw) to Lp,∞(Rn, w) or Lp(Rn,w), where B is a Young function and MB is the maximal operator associated with B.
HU Guo-En . WEIGHTED ESTIMATES WITH GENERAL WEIGHTS FOR MULTILINEAR CALDER´|ON-ZYGMUND OPERATORS[J]. Acta mathematica scientia, Series B, 2012 , 32(4) : 1529 -1544 . DOI: 10.1016/S0252-9602(12)60121-0
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