Karpushkin, V. N. A theorem concerning uniform estimates of oscillating integrals with the phase depending on two variables. (Russian. English summary) Zbl 0569.58033 Tr. Semin. Im. I. G. Petrovskogo 10, 150-169 (1984). 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 Cited in 4 ReviewsCited in 10 Documents MSC: 58J40 Pseudodifferential and Fourier integral operators on manifolds 35S05 Pseudodifferential operators as generalizations of partial differential operators 45G05 Singular nonlinear integral equations Keywords:uniform estimates for volumes; uniform estimates for oscillatory integrals PDFBibTeX XMLCite \textit{V. N. Karpushkin}, Tr. Semin. Im. I. G. Petrovskogo 10, 150--169 (1984; Zbl 0569.58033)