Multidimensional decay in the van der Corput lemma
Tom 208 / 2012
Studia Mathematica 208 (2012), 1-10
MSC: Primary 42B20; Secondary 42B37, 35L56.
DOI: 10.4064/sm208-1-1
Streszczenie
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.
