Uniform estimates for oscillatory integrals with homogeneous polynomial phases of degree 4

被引：3

作者：

Ruzhansky, Michael ^{[1
,2
]}

Safarov, Akbar R. ^{[3
,4
]}

Khasanov, Gafurjan A. ^{[4
]}

机构：

[1] Univ Ghent, Dept Math Anal Log & Discrete Math, Krijgslaan 281, Ghent, Belgium

[2] Queen Mary Univ London, Sch Math Sci, London, England

[3] Acad Sci Uzbek, Inst Math, Olmazor Dist Univ 46, Tashkent, Uzbekistan

[4] Samarkand State Univ, Dept Math, 15 Univ Blvd, Samarkand 140104, Uzbekistan

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2022年 / 12卷 / 06期

基金：

英国工程与自然科学研究理事会;

关键词：

Oscillatory integral; Phase function; Amplitude; CORPUT; VAN;

D O I：

10.1007/s13324-022-00747-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider the uniform estimates for oscillatory integrals with homogeneous polynomial phases of degree 4 in two variables. The obtained estimate is sharp and the result is an analogue of the more general theorem of Karpushkin (Proc I.G.Petrovsky Seminar 9:3-39, 1983) for sufficiently smooth functions, thus, in particular, removing the analyticity assumption.

引用

页数：15

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