Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A Toeplitz-type operator on Hardy spaces in the unit ball


Authors: Jordi Pau and Antti Perälä
Journal: Trans. Amer. Math. Soc. 373 (2020), 3031-3062
MSC (2010): Primary 47B35, 30H10
DOI: https://doi.org/10.1090/tran/8053
Published electronically: February 19, 2020
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study a Toeplitz-type operator $ Q_\mu $ between the holomorphic Hardy spaces $ H^p$ and $ H^q$ of the unit ball. Here the generating symbol $ \mu $ is assumed to be a positive Borel measure. This kind of operator is related to many classical mappings acting on Hardy spaces, such as composition operators, the Volterra-type integration operators, and Carleson embeddings. We completely characterize the boundedness and compactness of $ Q_\mu :H^p\to H^q$ for the full range $ 1<p,q<\infty $; and also describe the membership in the Schatten classes of $ H^2$. In the last section of the paper, we demonstrate the usefulness of $ Q_\mu $ through applications.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 47B35, 30H10

Retrieve articles in all journals with MSC (2010): 47B35, 30H10


Additional Information

Jordi Pau
Affiliation: Departament de Matemàtiques i Informàtica, Universitat de Barcelona, 08007 Barcelona, Catalonia, Spain
Email: jordi.pau@ub.edu

Antti Perälä
Affiliation: Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg SE-412 96, Sweden
Email: antti.perala@gu.se

DOI: https://doi.org/10.1090/tran/8053
Keywords: Hardy spaces, Toeplitz operators, tent spaces, Schatten classes
Received by editor(s): May 11, 2018
Received by editor(s) in revised form: February 15, 2019
Published electronically: February 19, 2020
Additional Notes: The first author was partially supported by DGICYT grant MTM2014-51834-P (MCyT/MEC) and the grant 2017SGR358 (Generalitat de Catalunya). The second author acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0445). Both authors were also supported by the grant MTM2017-83499-P (Ministerio de Educación y Ciencia).
Article copyright: © Copyright 2020 American Mathematical Society