Uniform estimates for oscillatory integrals with homogeneous polynomial phases of degree 4
Abstract
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 9:339, 1983) for sufficiently smooth functions, thus, in particular, removing the analyticity assumption.
 Publication:

Analysis and Mathematical Physics
 Pub Date:
 December 2022
 DOI:
 10.1007/s1332402200747w
 arXiv:
 arXiv:2205.06224
 Bibcode:
 2022AnMP...12..130R
 Keywords:

 Oscillatory integral;
 Phase function;
 Amplitude;
 Mathematical Physics