Anti-Wick quantization with symbols in 𝐿^{𝑝} spaces

Boggiatto, Paolo; Cordero, Elena

doi:10.1090/S0002-9939-02-06348-7

Anti-Wick quantization with symbols in $L^p$ spaces
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by Paolo Boggiatto and Elena Cordero PDF

Proc. Amer. Math. Soc. 130 (2002), 2679-2685 Request permission

Abstract:

We give a classification of pseudo-differential operators with anti-Wick symbols belonging to $L^p$ spaces: if $p=1$ the corresponding operator belongs to trace classes; if $1\leq p\leq 2$ we get Hilbert-Schmidt operators; finally, if $p<\infty$, the operator is compact. This classification cannot be improved, as shown by some examples.

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