Discrete analogues in harmonic analysis: Spherical averages

• 成果类型: Article
• 署名作者: Magyar, A; Stein, EM; Wainger, S
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3062154
• 发表日期: 2002
• 页码: 189-208
• 关键词: maximal operators

摘要

In this paper we prove an analogue in the discrete setting of Z(d), of the spherical maximal theorem for R-d. The methods used are two-fold: the application of certain sampling techniques, and ideas arising in the study of the number of representations of an integer as a sum of d squares, in particular, the circle method. The results we obtained are by necessity limited to d greater than or equal to 5, and moreover the range of p for the L-p estimates differs from its analogue in R-d.