TWO WEIGHT CHARACTERIZATIONS FOR THE MULTILINEAR LOCAL MAXIMAL OPERATORS  

作　　者：Yali PAN Qingying XUE 潘亚丽;薛庆营(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,China;Department of Mathematics,School of Information,Huaibei Normal University,Huaibei 235000,China;School of Mathematical Sciences,Beijing Normal University,Laboratory of Mathematics and Complex Systems,Ministry of Education,Beijing 100875,China)

机构地区：[1]College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,China [2]Department of Mathematics,School of Information,Huaibei Normal University,Huaibei 235000,China [3]School of Mathematical Sciences,Beijing Normal University,Laboratory of Mathematics and Complex Systems,Ministry of Education,Beijing 100875,China

出　　处：《Acta Mathematica Scientia》2021年第2期596-608,共13页数学物理学报（B辑英文版）

基　　金：supported partly by the Natural Science Foundation from the Education Department of Anhui Province(KJ2017A847);The second author was supported by NSFC(11671039,11871101);NSFC-DFG(11761131002).

摘　　要：Let 0<β<1 andΩbe a proper open and non-empty subset of R^(n).In this paper,the object of our investigation is the multilinear local maximal operator Mβ,defined by M_(β)((f))(x)=sup_(Q(∈)xQ∈Fβ)Π_(i=1)^m1/|Q|∫_(Q)|f_(i)(y_(i))|dy_(i),where F_(β)={Q(x,l):x∈Ω,l<βd(x,Ω^(c))},Q=Q(x,l)is denoted as a cube with sides parallel to the axes,and x and l denote its center and half its side length.Two-weight characterizations for the multilinear local maximal operator M_(β)are obtained.A formulation of the Carleson embedding theorem in the multilinear setting is proved.

关 键 词：Multilinear local maximal operators A_((p q))^(β)weights two-weight inequalities 

分 类 号：O177[理学—数学]