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arXiv · 1711.05215

On Fourier integral operators with Hölder-continuous phase

Elena Cordero·Fabio Nicola·Eva Primo
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Abstract

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 Hölder-type singularity at the origin. We prove boundedness in $L^1$ with a precise loss of decay depending on the Hölder 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 Hölder 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.

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Elena Cordero, Fabio Nicola, Eva Primo. 2017-11-14. On Fourier integral operators with Hölder-continuous phase. https://doi.org/10.1142/s0219530518500112

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