Products on Schatten-von Neumann classes and modulation spaces

Details Products on Schatten-von Neumann classes and modulation spaces Products on Schatten-von Neumann classes and modulation spaces

2009-02-16

arxiv.org/abs/0902.2654v1

Mathematics

Analysis of PDEs

38 pages

Scientific paper

We consider modulation space and spaces of Schatten-von Neumann symbols where corresponding pseudo-differential operators map one Hilbert space to another. We prove H\"older-Young and Young type results for such spaces under dilated convolutions and multiplications. We also prove continuity properties for such spaces under the twisted convolution, and the Weyl product. These results lead to continuity properties for twisted convolutions on Lebesgue spaces, e.{}g. $L^p_{(\omega)}$ is a twisted convolution algebra when $1\le p\le 2$ and appropriate weight $\omega$.

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