Communications in Mathematical Analysis

Hardy Classes and Symbols of Toeplitz Operators

Marco López-García and Salvador Pérez-Esteva

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 12 April 2018

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Toeplitz operators Hardy spaces Schatten classes


López-García, Marco; Pérez-Esteva, Salvador. Hardy Classes and Symbols of Toeplitz Operators. Commun. Math. Anal. 21 (2018), no. 1, 9--22.

Export citation