Communications in Mathematical Analysis

Hardy Classes and Symbols of Toeplitz Operators

Marco López-García and Salvador Pérez-Esteva

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Abstract

The purpose of this paper is to study functions in the unit disk $\mathbb D$ through the family of Toeplitz operators $\{T_{φdσ_{t}}\}_{t∈[0,1)}$, where $T_{φdσ_{t}}$ is the Toeplitz operator acting the Bergman space of $\mathbb D$ and where $dσ_t$ is the Lebesgue measure in the circle $tS^1$. In particular for $1\le p \lt \infty$ we characterize the harmonic functions $φ$ in the Hardy space $h^{p}(\mathbb D)$ by the growth in $t$ of the $p$-Schatten norms of $T_{φdσ_{t}}$. We also study the dependence in $t$ of the norm operator of $T_{adσ_{t}}$ when $a∈H^p_{at}$, the atomic Hardy space in the unit circle with $1/2 \lt p \le 1$.

Article information

Source
Commun. Math. Anal., Volume 21, Number 1 (2018), 9-22.

Dates
First available in Project Euclid: 12 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.cma/1523498575

Mathematical Reviews number (MathSciNet)
MR3789414

Zentralblatt MATH identifier
06873498

Subjects
Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Secondary: 30H10: Hardy spaces 42B30: $H^p$-spaces

Keywords
Toeplitz operators Hardy spaces Schatten classes

Citation

López-García, Marco; Pérez-Esteva, Salvador. Hardy Classes and Symbols of Toeplitz Operators. Commun. Math. Anal. 21 (2018), no. 1, 9--22. https://projecteuclid.org/euclid.cma/1523498575


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