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The dependence of uniform estimates of oscillating integrals on the amplitude. (English. Russian original) Zbl 0699.58020
Russ. Math. Surv. 44, No. 5, 198-200 (1989); translation from Usp. Mat. Nauk 44, No. 5(269), 163-164 (1989).
An oscillating integral I($$\tau$$,f,$$\phi)$$ is considered (here f: $${\mathbb{R}}^ n\to {\mathbb{R}}$$ is phase of corang 2 and $$\phi$$ is amplitude. A uniform estimate is given for having a possibility to find some new majorants for Maslov’s canonical operator in a neighborhood of caustic. Similar estimates are found for area and volume.
##### MSC:
 58C99 Calculus on manifolds; nonlinear operators
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