与退化Schrödinger算子有关的分数阶热核及Hardy空间刻画  

Fractional Heat Kernels Associated with Degenerate Schrödinger Operators and Characterizations of Hardy Space

作　　者：代甜甜 王志永 赵凯 DAI Tiantian;WANG Zhiyong;ZHAO Kai(School of Mathematics and Statistics,Qingdao University,Qingdao,Shandong,266071,P.R.China)

机构地区：[1]青岛大学数学与统计学院,青岛山东266071

出　　处：《数学进展》2022年第6期1037-1060,共24页Advances in Mathematics（China）

基　　金：Supported by Natural Science Foundation of Shandong Province(No.ZR2020MA004);NSFC(No.11871293)。

摘　　要：假定Lf(x)=−1/ω(x)∑i,j∂i(aij(⋅)∂jf)(x)+V(x)f(x)为退化Schrödinger算子,其中ω是来自Muckenhoupt class A_(2)的权.又设V是非负位势,属于与ω(x)dx有关的反Hölder不等式.基于分数阶热半群{e^(−tLα)}_(t>0)的正则性估计,我们通过两个面积函数S_(α)^(L)和g_(α)^(L)来刻画与L有关的Hardy空间.Assume that Lf(x)=−1ω(x)∑i,j∂i(aij(⋅)∂jf)(x)+V(x)f(x)is the degenerate Schrödinger operator,whereωis a weight from the Muckenhoupt class A2 and V is a nonnegative potential belonging to a certain reverse Hölder class related with the measureω(x)dx.By the regularity estimates of the fractional heat semigroup{e^(−tLα)}t>0,we introduce two square functions S_(α)^(L)and g_(α)^(L)to characterize the Hardy space associated with L.

关 键 词：HARDY空间 分数阶热核 退化薛定谔算子 原子 面积函数 

分 类 号：O174.2[理学—数学]