WEIGHTED ESTIMATES WITH GENERAL WEIGHTS FOR MULTILINEAR CALDER´|ON-ZYGMUND OPERATORS

doi:10.1016/S0252-9602(12)60121-0

Abstract

Abstract:

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, · · · , p_m ∈ [1,∞] and p ∈ (0,∞) with 1/p =∑^m_k₌₁1/p_k, then for any weight w, integer l with 1 ≤ l ≤ m, these operators are bounded from L^p¹ (Rⁿ, M_Bw) ×· · ·×L^pl(Rⁿ, M_Bw)×L^pl⁺¹ (Rⁿ, Mw)×· · ·×L^pm(Rⁿ, Mw) to L^p^,∞(Rⁿ, w) or Lp(Rn,w), where B is a Young function and MB is the maximal operator associated with B.

Key words: multilinear Calder´on-Zygmund operator, maximal operator, weighted norm inequality, Calder´on-Zygmund decomposition

CLC Number:

42B20

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.

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