Abstract
This paper gives a geometric method for uniformly bounding some classes of real oscillatory integrals with phase λ 1 P 1 + λ 2 P 2 , P 1 , P 2 real analytic or polynomial functions. A nontrivial decay rate uniform in (λ 1 , λ 2 ) is shown to exist and characterized geometrically when the mapping x → ( P 1 ( x ), P 2 ( x )) can be “uniformized”, an analog for maps of local uniformization for varieties.
Published Version
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