## Differential and Integral Equations

- Differential Integral Equations
- Volume 12, Number 2 (1999), 137-145.

### Uniform decay estimates for a class of oscillatory integrals and applications

#### Abstract

One dimensional oscillatory integrals of the type $\int^\infty _0 \xi ^\alpha \rm\exp \big[it(p(\xi )-\xi x)\big]\rm {d}\xi $ are considered, where $p(\xi )$ is a real polynomial of degree $m\geq 3$. Long-time decay and global smoothing estimates are established, as well as short-time behavior as $t\to 0$. The results are applied to the fundamental solutions of a class of linearized Kadomtsev-Petviashvili equations with higher dispersion

#### Article information

**Source**

Differential Integral Equations, Volume 12, Number 2 (1999), 137-145.

**Dates**

First available in Project Euclid: 29 April 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1367265625

**Mathematical Reviews number (MathSciNet)**

MR1672730

**Zentralblatt MATH identifier**

1016.35006

**Subjects**

Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]

Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 42B25: Maximal functions, Littlewood-Paley theory

#### Citation

Ben-Artzi, M.; Saut, J.-C. Uniform decay estimates for a class of oscillatory integrals and applications. Differential Integral Equations 12 (1999), no. 2, 137--145. https://projecteuclid.org/euclid.die/1367265625