# Some oscillatory integral estimates via real analysis

@article{Gilula2016SomeOI, title={Some oscillatory integral estimates via real analysis}, author={Maxim Gilula}, journal={Mathematische Zeitschrift}, year={2016}, volume={289}, pages={377-403} }

We study oscillatory integrals in several variables with analytic, smooth, or $$C^k$$Ck phases satisfying a nondegeneracy condition attributed to Varchenko. With only real analytic methods, Varchenko’s sharp estimates are rediscovered and generalized. The same methods are pushed further to obtain full asymptotic expansions of such integrals with analytic and smooth phases, and finite expansions with error assuming the phase is only $$C^k$$Ck. The Newton polyhedron appears naturally in the… Expand

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