Karpushkin, V. N. 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. Reviewer: G.V.Khmelevskaya Plotnikova MSC: 58C99 Calculus on manifolds; nonlinear operators Keywords:uniform estimate majorants; oscillating integral; Maslov’s canonical operator PDF BibTeX XML Cite \textit{V. N. Karpushkin}, Russ. Math. Surv. 44, No. 5, 198--200 (1989; Zbl 0699.58020); translation from Usp. Mat. Nauk 44, No. 5(269), 163--164 (1989) Full Text: DOI