# Multidimensional decay in the van der Corput lemma

Studia Mathematica (2012)

- Volume: 208, Issue: 1, page 1-10
- ISSN: 0039-3223

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topMichael Ruzhansky. "Multidimensional decay in the van der Corput lemma." Studia Mathematica 208.1 (2012): 1-10. <http://eudml.org/doc/285789>.

@article{MichaelRuzhansky2012,

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.},

author = {Michael Ruzhansky},

journal = {Studia Mathematica},

keywords = {van der Corput lemma; stationary phase; sublevel set estimates; multidimensional decay of oscillatory integrals, degenerate stationary points},

language = {eng},

number = {1},

pages = {1-10},

title = {Multidimensional decay in the van der Corput lemma},

url = {http://eudml.org/doc/285789},

volume = {208},

year = {2012},

}

TY - JOUR

AU - Michael Ruzhansky

TI - Multidimensional decay in the van der Corput lemma

JO - Studia Mathematica

PY - 2012

VL - 208

IS - 1

SP - 1

EP - 10

AB - 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.

LA - eng

KW - van der Corput lemma; stationary phase; sublevel set estimates; multidimensional decay of oscillatory integrals, degenerate stationary points

UR - http://eudml.org/doc/285789

ER -

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