Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

Discrete Analogues in Harmonic Analysis: Spherical Averages

A. Magyar, E. M. Stein and S. Wainger
Annals of Mathematics
Second Series, Vol. 155, No. 1 (Jan., 2002), pp. 189-208
Published by: Annals of Mathematics
DOI: 10.2307/3062154
Stable URL: http://www.jstor.org/stable/3062154
Page Count: 20
  • Read Online (Free)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Discrete Analogues in Harmonic Analysis: Spherical Averages
Preview not available

Abstract

In this paper we prove an analogue in the discrete setting of Zd, of the spherical maximal theorem for Rd. 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 ≥ 5, and moreover the range of p for the Lp estimates differs from its analogue in Rd.

Page Thumbnails

  • Thumbnail: Page 
[189]
    [189]
  • Thumbnail: Page 
190
    190
  • Thumbnail: Page 
191
    191
  • Thumbnail: Page 
192
    192
  • Thumbnail: Page 
193
    193
  • Thumbnail: Page 
194
    194
  • Thumbnail: Page 
195
    195
  • Thumbnail: Page 
196
    196
  • Thumbnail: Page 
197
    197
  • Thumbnail: Page 
198
    198
  • Thumbnail: Page 
199
    199
  • Thumbnail: Page 
200
    200
  • Thumbnail: Page 
201
    201
  • Thumbnail: Page 
202
    202
  • Thumbnail: Page 
203
    203
  • Thumbnail: Page 
204
    204
  • Thumbnail: Page 
205
    205
  • Thumbnail: Page 
206
    206
  • Thumbnail: Page 
207
    207
  • Thumbnail: Page 
208
    208