On the action of Hankel and Toeplitz operators on some function spaces
type: Item
instance of: scholarly article
title: On the action of Hankel and Toeplitz operators on some function spaces
zbMATH Open document ID: 0579.47022
DOI: 10.1215/S0012-7094-84-05142-1
author: Jaak Peetre
author: Stephen Semmes
author: Svante Janson
published in: Duke Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: Hardy and Toeplitz operators are usually considered on the (Hilbert) Hardy space \(H^ 2=H^ 2({\mathbb{T}})\), \({\mathbb{T}}\) unit circumference. In this very important paper we consider their action on some other function spaces, especially, \(H^ p\), \(0<p<\infty\) and \({\mathcal B}\) (Bloch space). If \(p=1\), the condition for boundedness on the symbol b of a Hankel operator reads \(\bar Pb\in \bar {\mathcal B}\) (P Riesz projection). We treat further Hankel operators with Bloch symbols. Such operators act from \(B_ p^{0,1}\) into \(B_ p^{0,\infty}\). In the last section the boundedness of Toeplitz symbols is established for a quite general class of spaces.
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 3927704
zbMATH Keywords: Besov space
zbMATH Keywords: BMO
zbMATH Keywords: Hardy and Toeplitz operators
zbMATH Keywords: Hardy space
zbMATH Keywords: Bloch space
zbMATH Keywords: Hankel operators with Bloch symbols
zbMATH Keywords: boundedness of Toeplitz symbols
MaRDI profile type: Publication
cites work: Q4043323
cites work: Q3346810
cites work: Q4112938
cites work: A real variable characterization of $H^{p}$
cites work: Factorization theorems for Hardy spaces in several variables
cites work: Q5618011
cites work: \(H^p\) spaces of several variables
cites work: Q3922907
cites work: The atomic decomposition for Hardy spaces in several complex variables
cites work: Factorization theorems for functions in the Bergman spaces
cites work: On functions with conditions on the mean oscillation
cites work: Generalizations of Lipschitz spaces and an application to Hardy spaces and bounded mean oscillation
cites work: Schatten classes and commutators of singular integral operators
cites work: Q3671690
cites work: Theory of multipliers in spaces of differentiable functions
cites work: A generalization of the Fourier-Borel transformation for the analytic functionals with non convex carrier
cites work: Q4129323
cites work: On the theory of \({\mathcal L}_{p, \lambda}\) spaces
cites work: Q3660387
cites work: An Extremal Property of the Bloch Space
cites work: Q5607484
cites work: Q4182986
cites work: Bounded Toeplitz Operators on H 1 and Applications of the Duality Between H 1 and the Functions of Bounded Mean Oscillation
cites work: Q3336200
cites work: On the compactness of operators of Hankel type
full work available at URL: s0012-7094-84-05142-1
OpenAlex ID: W1588272336
description: scientific article; zbMATH DE number 3927704