Pointwise van der Corput lemma for functions of several variables
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 wordsvan der Corput lemma oscillatory integral asymptotic estimate
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