To the memory of L. R. Volevich
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.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 43, No. 1, pp. 91–93, 2009
Original Russian Text Copyright © by Michael Ruzhansky
The author was supported by the Leverhulme Research Fellowship and by EPSRC grant EP/E062873/01.
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Ruzhansky, M. Pointwise van der Corput lemma for functions of several variables. Funct Anal Its Appl 43, 75–77 (2009). https://doi.org/10.1007/s10688-009-0010-5
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DOI: https://doi.org/10.1007/s10688-009-0010-5