Multidimensional decay in the van der Corput lemma

Michael 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 -