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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm208-1-1,
author = {Michael Ruzhansky},
title = {Multidimensional decay in the van der Corput lemma},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {1-10},
zbl = {1248.42019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm208-1-1}
}
Michael Ruzhansky. Multidimensional decay in the van der Corput lemma. Studia Mathematica, Tome 209 (2012) pp. 1-10. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm208-1-1/