6533b83afe1ef96bd12a7020
RESEARCH PRODUCT
On Fourier integral operators with Hölder-continuous phase
Elena CorderoEva PrimoFabio Nicolasubject
Modulation spaceApplied Mathematics010102 general mathematicsMathematical analysisShort-time Fourier transformPhase (waves)Hölder conditionFourier integral operators; modulation spaces; short-time Fourier transform; Analysis; Applied Mathematics01 natural sciencesBoltzmann equationFourier integral operatorMathematics - Functional Analysis010101 applied mathematicsSingularityshort-time Fourier transformFourier integral operators0101 mathematicsLp spacemodulation spacesMathematical PhysicsAnalysisMathematicsdescription
We study continuity properties in Lebesgue spaces for a class of Fourier integral operators arising in the study of the Boltzmann equation. The phase has a H\"older-type singularity at the origin. We prove boundedness in $L^1$ with a precise loss of decay depending on the H\"older exponent, and we show by counterexamples that a loss occurs even in the case of smooth phases. The results can be seen as a quantitative version of the Beurling-Helson theorem for changes of variables with a H\"older singularity at the origin. The continuity in $L^2$ is studied as well by providing sufficient conditions and relevant counterexamples. The proofs rely on techniques from Time-frequency Analysis.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-01-01 |