Harmonic Analysis Related to Homogeneous Varieties in Three Dimensional Vector Spaces over Finite Fields

Canadian Journal of Mathematics

Chun-Yen Shen¹  Doowon Koh¹ 

DOI  :  10.4153/CJM-2011-089-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this paper we study the extension problem, theaveraging problem, and the generalized Erdős-Falconer distanceproblem associated with arbitrary homogeneous varieties in threedimensional vector spaces over finite fields. In the case when thevarieties do not contain any plane passing through the origin, weobtain the best possible results on the aforementioned three problems. Inparticular, our result on the extension problem modestly generalizesthe result by Mockenhaupt and Tao who studied the particular conicalextension problem. In addition, investigating the Fourier decay onhomogeneous varieties enables us to give complete mapping propertiesof averaging operators. Moreover, we improve the size condition on aset such that the cardinality of its distance set is nontrivial.

【 授权许可】

Unknown