GEOMETRY AND HARDY SPACES

2018-01-02

GEOMETRY AND HARDY SPACES


报告人:Yongsheng Han   Auburn University


摘要:It was well known that geometric considerations enter in a decisive way in many questions of analysis. As Meyer, the recipient of the 2017 Abel Prize, remarked ``One is amazed by the dramatic changes that occurred in analysis during the twentieth century. In the 1930s complex methods and Fourier series played a seminal role. After many improvements, mostly achieved by the Calderón-Zygmund school, the action takes place today on spaces of homogeneous type. No group structure is available, the Fourier transform is missing, but a version of harmonic analysis is still present. Indeed the geometry is conducting the analysis." In this talk, we will concentrate on a question that how the geometrical considerations play a crucial role in the theory of the Hardy space. We shall begin by recalling the theory of the Hardy space on the Euclidean space. To be precise, we will attempt to give a broad overview of the characterizations of the Hardy space via the Littlewood-Paley theory and atomic decomposition. we then take up these same topics in more general settings such as domains in Rnor space of homogeneous type (X, d, μ) in the sense of Coifman and Weiss, and discuss the geometrical considerations on the quasi-metric d and the measure μ.


时间和地点:201818日下午2点30分,数学学院第七教室


邀请人:孙文昌



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