A Local Tb Theorem for Square Functions and Parabolic Layer Potentials  

作　　者：Zhi Dan WANG Guo Ming ZHANG 

机构地区：[1]School of Physical and Mathematical Sciences,Nanjing Tech University,Nanjing 211816,P.R.China [2]Frontiers Science Center for Nonlinear Expectations,Ministry of Eduction,Research Center for Mathematics and Interdisciplinary Sciences,Shandong University,Qingdao,266237,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第8期1941-1966,共26页数学学报（英文版）

基　　金：Supported by Natural Science Foundation of Jiangsu Province of China(Grant No.BK20220324);Natural Science Research of Jiangsu Higher Education Institutions of China(Grant No.22KJB110016)。

摘　　要：In this paper,we give a locally parabolic version of Tb theorem for a class of vector-valued operators with off-diagonal decay in L^(2) and certain quasi-orthogonality on a subspace of L^(2),in which the testing functions themselves are also vector-valued.As an application,we establish the boundedness of layer potentials related to parabolic operators in divergence form,defined in the upper half-space Rn+2+:={(x,t,λ)∈R^(n+1)×(0,∞)},with uniformly complex elliptic,L^(∞),t,λ-independent coefficients,and satisfying the De Giorgi/Nash estimates.

关 键 词：Local Tb theorems Calderon-Littlewood-Paley family Parabolic layer potentials Carleson measure estimates 

分 类 号：O177[理学—数学]