Geodesic
Multidimensional decay in the van der Corput lemma
Michael Ruzhansky 1
1 Department of Mathematics Imperial College London 180 Queen's Gate London SW7 2AZ, United Kingdom
Studia Mathematica, Tome 208 (2012) no. 1, pp. 1-10 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We establish a multidimensional decay of oscillatory integrals with degenerate stationary points, gaining the decay with respect to all space variables. This bridges the gap between the one-dimensional decay for degenerate stationary points given by the classical van der Corput lemma and the multidimensional decay for non-degenerate stationary points given by the stationary phase method. Complex-valued phase functions as well as phases and amplitudes of limited regularity are considered. Conditions for estimates to be uniform in parameter are also given.
DOI : 10.4064/sm208-1-1
Keywords: establish multidimensional decay oscillatory integrals degenerate stationary points gaining decay respect space variables bridges gap between one dimensional decay degenerate stationary points given classical van der corput lemma multidimensional decay non degenerate stationary points given stationary phase method complex valued phase functions phases amplitudes limited regularity considered conditions estimates uniform parameter given

Michael Ruzhansky  1

1 Department of Mathematics Imperial College London 180 Queen's Gate London SW7 2AZ, United Kingdom 
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Michael Ruzhansky. Multidimensional decay in the van der Corput lemma. Studia Mathematica, Tome 208 (2012) no. 1, pp. 1-10. doi: 10.4064/sm208-1-1

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