Abstract
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.
Mathematics Subject Classification (2010). Primary 35S05, 47B10, 46F99, 47B37, 44A35; Secondary 42B35, 47B35.
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Toft, J. (2013). Multiplication Properties in Gelfand–Shilov Pseudo-differential Calculus. In: Molahajloo, S., Pilipović, S., Toft, J., Wong, M. (eds) Pseudo-Differential Operators, Generalized Functions and Asymptotics. Operator Theory: Advances and Applications, vol 231. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0585-8_7
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DOI: https://doi.org/10.1007/978-3-0348-0585-8_7
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