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Toeplitz Operators with Positive Measures on Harmonic Fock Spaces

Xue Gou, Xin Hu, Sui Huang

Abstract

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

Toeplitz Operators with Positive Measures on Harmonic Fock Spaces

Abstract

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

Paper Structure

This paper contains 4 sections, 14 theorems, 63 equations.

Table of Contents

  1. Introduction
  2. Harmonic Fock-Carleson Measures
  3. Boundedness and Compactness of $T_\mu$
  4. Schatten Class $S_p$ of $T_\mu$

Key Result

Lemma 2.1

The norm of $h_{z}(\omega)$ is not more than $\sqrt{2}$ in $F_{h}^{p}$, where $p\geq1$.

Theorems & Definitions (24)

  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • Theorem 2.1
  • proof
  • Theorem 2.2
  • proof
  • ...and 14 more