Gains of integrability and local smoothing effects for quadratic evolution equations
Résumé
We characterize geometrically the semigroups generated by non-selfadjoint quadratic differential operators $(e^{-tq^w})_{t\geq 0}$ enjoying local smoothing effects and providing gains of integrability. More precisely, we prove that the evolution operators $e^{-tq^w}$ map $L^{\mathfrak{p}}$ on $L^{\mathfrak{q}} \cap C^\infty$, for all $1\leq \mathfrak{p} \leq \mathfrak{q} \leq \infty$, if and only if the singular space of the quadratic operator $q^w$ is included in the graph of a linear map. We also provide quantitative estimates for the associated operator norms in the short-time asymptotics $0
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https://hal.science/hal-03437144
Soumis le : mardi 14 mars 2023-15:46:34
Dernière modification le : jeudi 14 mars 2024-03:16:00
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Identifiants
- HAL Id : hal-03437144 , version 2
- ARXIV : 2111.11254
- DOI : 10.1016/j.jfa.2023.110119
Citer
Paul Alphonse, Joackim Bernier. Gains of integrability and local smoothing effects for quadratic evolution equations. Journal of Functional Analysis, 2023, 285 (10), ⟨10.1016/j.jfa.2023.110119⟩. ⟨hal-03437144v2⟩
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