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Brief communications

Pointwise van der Corput Lemma for Functions of Several Variables

M. V. Ruzhanskii

Imperial College London

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.

Keywords: van der Corput lemma, oscillatory integral, asymptotic estimate.

UDC: 517

Received: 13.04.2007

DOI: 10.4213/faa2937

 English version: Functional Analysis and Its Applications, 2009, 43:1, 75–77

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