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

@article{Ruzhansky2022UniformEF, title={Uniform estimates for oscillatory integrals with homogeneous polynomial phases of degree 4}, author={Michael Ruzhansky and A. R. Safarov and G. A. Khasanov}, journal={Analysis and Mathematical Physics}, year={2022}, volume={12} }

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.

## One Citation

### Oscillatory integrals for Mittag-Leffler functions with two variables

- Mathematics
- 2023

. In this paper we consider the problem of estimation of oscillatory integrals with Mittag-Leﬄer functions in two variables. The generalisation is that we replace the exponential function with the…

## References

SHOWING 1-10 OF 19 REFERENCES

### On the growth and stability of real-analytic functions

- Mathematics
- 1999

This paper addresses the issue of whether integrals of real-analytic functions remain finite under small deformations. An approach based on uniform estimates for certain classes of one-dimensional…

### INVARIANT ESTIMATES OF TWO-DIMENSIONAL TRIGONOMETRIC INTEGRALS

- Mathematics
- 1990

A uniform estimate is obtained for two-dimensional oscillating integrals with polynomial phase in terms of certain invariants of subgroups of affine groups. Bibliography: 22 titles.

### Fourier Integrals in Classical Analysis

- Mathematics
- 1993

Background 1. Stationary phase 2. Non-homogeneous oscillatory integral operators 3. Pseudo-differential operators 4. The half-wave operator and functions of pseudo-differential operators 5. Lp…

### Pointwise van der Corput Lemma for Functions of Several Variables ∗

- Mathematics
- 2009

A multidimensional version of the well-known van der Corput lemma is presented. A class of phase functions is described for which the corresponding oscillatory integrals satisfy a multidimensional…

### Newton polyhedra and estimation of oscillating integrals

- Mathematics
- 1976

The aim of this paper is to calculate the principal term of the asymptotic expansion of an oscillating integral in a neighborhood of a singular critical point of the phase in terms of Newton's…

### Uniform Estimates for the Fourier Transform of Surface Carried Measures in ℝ3 and an Application to Fourier Restriction

- Mathematics
- 2010

AbstractLet S be a hypersurface in ${\Bbb{R}}^{3}$ which is the graph of a smooth, finite type function φ, and let μ=ρ
dσ be a surface carried measure on S, where dσ denotes the surface element on…

### Multidimensional decay in van der Corput lemma

- Mathematics
- 2007

In this paper we present a multidimensional version of the van der Corput lemma where the decay of the oscillatory integral is gained with respect to all space variables, connecting the standard…

### Harmonic analysis

- Engineering2004 IEEE Electro/Information Technology Conference
- 2004

A method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms, of a signal having an arbitrary dimension of the digital representation by reducing the transform to a vector-to-circulant matrix multiplying.

### Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra

- Mathematics
- 2016

This is the first book to present a complete characterization of Stein-Tomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all…

### Singularities of differentiable maps

- 2011

© Publications mathématiques de l’I.H.É.S., 1967, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://…