Discrete analogues in harmonic analysis: Spherical averages

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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.
20 pages, published version

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Classical Analysis and ODEs

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http://salesiana.dossiersoluciones.com/handle/123456789/72548

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0409365
 http://arxiv.org/abs/math/0409365
 Ann. of Math. (2), Vol. 155, (2002), no. 1, 189--208

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