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Toeplitz Operators with Positive Measures on Harmonic Fock Spaces

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arxiv 2410.06538 v1 pith:EODO4NIO submitted 2024-10-09 math.FA

Xue Gou , Xin Hu , Sui Huang This is my paper · ORCID
classification math.FA
keywords operatorsfockharmonicmeasurespositivespacestoeplitzbasic
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abstract

In this paper, we study the basic properties of Toeplitz Operators with positive measures $\mu$ on harmonic Fock spaces. We prove equivalent conditions for boundedness, compactness and Schatten classes $S_{p}$ of $T_{\mu}$ by using the methods of Berezin transform of operators.

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  1. Positive Toeplitz operators on pluriharmonic Fock space: Schatten class criteria and sharp norm comparisons

    math.FA 2026-08 accept novelty 7.0 of 10

    Positive Toeplitz operators on pluriharmonic Fock space belong to the same Schatten classes as their holomorphic counterparts, with sharp norm comparison constants and an exact trace identity.

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