Discrete analogues in harmonic analysis: Spherical averages
经典分析与常微分方程
2007-05-23 v1
摘要
In this paper we prove an analogue in the discrete setting of \Bbb Z^d, of the spherical maximal theorem for \Bbb 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 \ge 5, and moreover the range of p for the L^p estimates differs from its analogue in \Bbb R^d.
引用
@article{arxiv.math/0409365,
title = {Discrete analogues in harmonic analysis: Spherical averages},
author = {A. Magyar and E. M. Stein and S. Wainger},
journal= {arXiv preprint arXiv:math/0409365},
year = {2007}
}
备注
20 pages, published version