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Published in:
2013 | OriginalPaper | Chapter
Multiplication Properties in Gelfand–Shilov Pseudo-differential Calculus
Author : Joachim Toft
Published in: Pseudo-Differential Operators, Generalized Functions and Asymptotics
Publisher: Springer Basel
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We consider modulation space and spaces of Schatten–von Neumann symbols where corresponding pseudo-differential operators map one Hilbert space to another. We prove Hölder–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
(ω)
is a twisted convolution algebra when 1 ≤
p
≤ 2 and appropriate weight
ω
.