A van der Corput lemma for the p-adic numbers

Proceedings of the American Mathematical Society

Volumn 133, Issue 12, 2005, Pages 3525-3534

  Rogers, Keith M ^a,b  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

Oscillatory integrals; P adic; Van der Corput lemma

Indexed keywords

EID: 29144446836     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-05-07919-0     Document Type: Article

References (10)

1. G.I. Arhipov, A.A. Karacuba and V.M. Čubarikov, Trigonometric integrals, Math. USSR Izvestija 15 (1980), 211-239.
2. E. Breuillard and T. Gelander, A topological Tits alternative, to appear, Ann. Math.
3. A. Carbery, M. Christ and J. Wright, Multidimensional van der Corput and sublevel set estimates, J. Amer. Math. Soc. 12 (1999), no. 4, 981-1015. MR1683156 (2000h:42010)
4. J.G. van der Corput, Zahlentheoretische abschätzungen, Math. Ann. 84 (1921), 53-79.
5. N. Koblitz, p-adic analysis: a short course on recent work, Cambridge Univ. Press, Cambridge, 1980. MR0591682 (82c:12014)
6. K. M. Rogers, Sharp van der Corput estimates and minimal divided differences, this issue.
7. K.M. Rogers, Maximal averages along curves over the p-adic numbers, to appear, Bull, Austral. Math. Soc.
8. E. M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, Princeton, NJ, 1993. MR1232192 (95c:42002)
9. M. H. Taibleson, Fourier analysis on local fields, Princeton Univ. Press, Princeton, N.J., 1975. MR0487295 (58:6943)
10. J. Wright, p-Adic van der Corput lemmas, unpublished manuscript.