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Zbl 1236.47046
Luef, Franz; Rahbani, Zohreh
On pseudodifferential operators with symbols in generalized Shubin classes and an application to Landau-Weyl operators. (English)
[J] Banach J. Math. Anal. 5, No. 2, 59-72, electronic only (2011). ISSN 1735-8787/e

Let $L_a$ be the Weyl operator with $a$ the Weyl symbol, and let $\widetilde{L_a}$ be the Landau-Weyl operator. The authors assume that the function $a$ above belongs to a modulation space with radial symmetric weight. They show that, if the exponent of the modulation space satisfies a certain condition, then the Weyl operator and the Landau-Weyl operator both belong to the Schatten-von Neumann class of bounded linear operators by studying the behavior of the singular values of the Weyl operator and of the Landau-Weyl operator. \par Throughout the paper, the authors put emphasis on the importance of the modulation space.
[Shuji Watanabe (Maebashi)]

MSC 2000:: *47G30 Pseudodifferential operators
42C15 Series and expansions in general function systems
42C40 Wavelets
47B10 Operators defined by summability properties

Keywords: modulation spaces; pseudodifferential operators; Wilson basis; Shubin classes

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