Geodesic
Pointwise van der Corput Lemma for Functions of Several Variables
Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 1, pp. 91-93

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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. 
@article{FAA_2009_43_1_a8,
     author = {M. V. Ruzhanskii},
     title = {Pointwise van der {Corput} {Lemma} for {Functions} of {Several} {Variables}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {91--93},
     publisher = {mathdoc},
     volume = {43},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2009_43_1_a8/}
}
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M. V. Ruzhanskii. Pointwise van der Corput Lemma for Functions of Several Variables. Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 1, pp. 91-93. http://geodesic.mathdoc.fr/item/FAA_2009_43_1_a8/