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Functional Analysis and Its Applications

, Volume 43, Issue 1, pp 75–77 | Cite as

Pointwise van der Corput lemma for functions of several variables

  • Michael RuzhanskyEmail author
Brief Communications

Abstract

A multidimensional version of the well-known van der Corput lemma is presented. A class of phase functions is described for which the corresponding oscillatory integrals satisfy a multidimensional decay estimate. The obtained estimates are uniform with respect to parameters on which the phases and amplitudes may depend.

Key words

van der Corput lemma oscillatory integral asymptotic estimate 

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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Imperial College LondonLondonUK

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