Weak type(1, 1) of the Riesz transform on some direct product manifolds with exponential volume growth  

作　　者：Hong-Quan Li Jie-Xiang Zhu 

机构地区：[1]School of Mathematical Sciences,Fudan University,Shanghai,200433,China [2]Center for Applied Mathematics,Tianjin University,Tianjin,300072,China

出　　处：《Science China Mathematics》2024年第7期1599-1622,共24页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 12271102, 11625102, 11831004 and 11921001);supported by the National Key R&D Program of China (Grant Nos. 2022YFA1006000 and 2020YFA0712900)。

摘　　要：In this paper, we are concerned with the Riesz transform on the direct product manifold H^(n)× M,where H^(n) is the n-dimensional real hyperbolic space, and M is a connected complete non-compact Riemannian manifold satisfying the volume doubling property and generalized Gaussian or sub-Gaussian upper estimates for the heat kernel. We establish its weak type(1, 1) property. In addition, we obtain the weak type(1, 1) of the heat maximal operator in the same setting. Our arguments also work for a large class of direct product manifolds with exponential volume growth. Particularly, we provide a simpler proof of weak type(1, 1) boundedness of some operators considered in the work of Li et al.(2016).

关 键 词：Riesz transform heat kernel direct product real hyperbolic space 

分 类 号：O186.12[理学—数学]