Geodesic
Multidimensional van der Corput and sublevel set estimates
Carbery, Anthony 1   ; Christ, Michael 2   ; Wright, James 3
1 Department of Mathematics & Statistics, University of Edinburgh, King’s Buildings, Edinburgh EH9 3JZ, Scotland, United Kingdom
2 Department of Mathematics, University of California, Berkeley, California 94720-3840
3 Department of Mathematics, University of New South Wales, 2052 Sydney, New South Wales, Australia
Journal of the American Mathematical Society, Tome 12 (1999) no. 4, pp. 981-1015 Cet article a éte moissonné depuis la source American Mathematical Society

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Van der Corput’s lemma gives an upper bound for one-dimensional oscillatory integrals that depends only on a lower bound for some derivative of the phase, not on any upper bound of any sort. We establish generalizations to higher dimensions, in which the only hypothesis is that a partial derivative of the phase is assumed bounded below by a positive constant. Analogous upper bounds for measures of sublevel sets are also obtained. The analysis, particularly for the sublevel set estimates, has a more combinatorial flavour than in the one-dimensional case.
DOI : 10.1090/S0894-0347-99-00309-4

Carbery, Anthony  1   ; Christ, Michael  2   ; Wright, James  3

1 Department of Mathematics & Statistics, University of Edinburgh, King’s Buildings, Edinburgh EH9 3JZ, Scotland, United Kingdom
2 Department of Mathematics, University of California, Berkeley, California 94720-3840
3 Department of Mathematics, University of New South Wales, 2052 Sydney, New South Wales, Australia 
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Carbery, Anthony; Christ, Michael; Wright, James. Multidimensional van der Corput and sublevel set estimates. Journal of the American Mathematical Society, Tome 12 (1999) no. 4, pp. 981-1015. doi: 10.1090/S0894-0347-99-00309-4

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