Multidimensional decay in the van der Corput lemma

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Title: Multidimensional decay in the van der Corput lemma
Author(s): Ruzhansky, M
Item Type: Journal Article
Abstract: 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.
Publication Date: 31-Jan-2012
Date of Acceptance: 1-Jan-2012
URI: http://hdl.handle.net/10044/1/55317
DOI: https://dx.doi.org/10.4064/sm208-1-1
ISSN: 0039-3223
Publisher: Polskiej Akademii Nauk, Instytut Matematyczny
Start Page: 1
End Page: 10
Journal / Book Title: Studia Mathematica
Volume: 208
Issue: 1
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/E062873/1
EP/G007233/1
Copyright Statement: Michael Ruzhansky. Studia Mathematica 208 (2012), 1-10
Keywords: Science & Technology
Physical Sciences
Mathematics
van der Corput lemma
stationary phase
sublevel set estimates
HYPERBOLIC-EQUATIONS
SET
SYSTEMS
math.AP
math.AP
math.FA
42B15, 35S30
Science & Technology
Physical Sciences
Mathematics
van der Corput lemma
stationary phase
sublevel set estimates
HYPERBOLIC-EQUATIONS
SET
SYSTEMS
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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