On trace ideal weighted composition operators on weighted Fock spaces (Q895805)

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scientific article; zbMATH DE number 6516549
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On trace ideal weighted composition operators on weighted Fock spaces
scientific article; zbMATH DE number 6516549

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    On trace ideal weighted composition operators on weighted Fock spaces (English)
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    4 December 2015
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    In his previous paper [Arch. Math. 101, No. 4, 349--360 (2013; Zbl 1281.32010)] the author gave conditions for weighted composition operators on Fock-Sobolev spaces or on Fock spaces with radial weight to be in the Schatten ideals \(\mathcal{S}_p\). Necessary and sufficient conditions were expressed as \(L^p\) integrability conditions for \(p\geq2\) using a link with Toeplitz operators being in \(\mathcal{S}_{p/2}\). Since the latter is not available for \(p<2\), in this paper, a different approach is used to include the gap \(0<p<2\) and give the analysis for all \(0<p<\infty\).
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    Fock-Sobolev spaces
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    weighted Fock spaces
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    weighted composition operator
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    Schatten class membership
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