Multidimensional decay in the van der Corput lemma

• Autorzy: Michael Ruzhansky
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42B37: Harmonic analysis and PDE
• 35L56: Initial value problems for higher-order hyperbolic systems
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 208
• Numer: 1
• Strony: 1-10

Daty

wydano

2012

Twórcy

autor

Michael Ruzhansky

• Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, United Kingdom

Identyfikatory

DOI

10.4064/sm208-1-1