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A theorem concerning uniform estimates of oscillating integrals with the phase depending on two variables. (Russian. English summary) Zbl 0569.58033

Author’s summary: ”It is proved in the article that an oscillatory integral with a phase dependent function on two variables admits an estimate from above, uniform with respect to small parameters, by means of a quantity proportional to the value of the integral at zero values of the parameters. An analogous uniform estimate is obtained for volumes. The hypothesis about the semi-continuity of the height for functions of two variables due to V. I. Arnol’d is also proved.”
Reviewer: B.Nowak

MSC:

58J40 Pseudodifferential and Fourier integral operators on manifolds
35S05 Pseudodifferential operators as generalizations of partial differential operators
45G05 Singular nonlinear integral equations
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