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arXiv · 0807.2380

Boundedness of Schroedinger type propagators on modulation spaces

Elena Cordero·Fabio Nicola
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Abstract

It is known that Fourier integral operators arising when solving Schrödinger-type operators are bounded on the modulation spaces $\cM^{p,q}$, for $1\leq p=q\leq\infty$, provided their symbols belong to the Sjöstrand class $M^{\infty,1}$. However, they generally fail to be bounded on $\cM^{p,q}$ for $p\not=q$. In this paper we study several additional conditions, to be imposed on the phase or on the symbol, which guarantee the boundedness on $\cM^{p,q}$ for $p\not=q$, and between $\cM^{p,q}\to\cM^{q,p}$, $1\leq q< p\leq\infty$. We also study similar problems for operators acting on Wiener amalgam spaces, recapturing, in particular, some recent results for metaplectic operators. Our arguments make heavily use of the uncertainty principle.

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Elena Cordero, Fabio Nicola. 2009-08-28. Boundedness of Schroedinger type propagators on modulation spaces. https://arxiv.org/abs/0807.2380

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