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

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外文摘要：In this paper,we are concerned with the Riesz transform on the direct product manifold Hn × M,where Hn 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).

外文关键词：

Riesz transformheat kerneldirect productreal hyperbolic space

作者：

Hong-Quan Li、Jie-Xiang Zhu

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作者单位：

School of Mathematical Sciences,Fudan University,Shanghai 200433,China

Center for Applied Mathematics,Tianjin University,Tianjin 300072,China

基金：

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Key R&D Program of ChinaNational Key R&D Program of China

项目编号：

122711021162510211831004119210012022YFA10060002020YFA0712900

出版年：

2024

DOI：

10.1007/s11425-022-2134-6

中国科学:数学(英文版)

中国科学院

中国科学:数学(英文版)

CSTPCD

影响因子：0.36

ISSN：1674-7283

年,卷(期)：2024.67(7)