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.
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页数：15
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