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Generalized integration operators on Hardy spaces


Author: Nikolaos Chalmoukis
Journal: Proc. Amer. Math. Soc. 148 (2020), 3325-3337
MSC (2010): Primary 30H10; Secondary 30H35, 47G10
DOI: https://doi.org/10.1090/proc/15016
Published electronically: May 8, 2020
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Abstract: We introduce a natural generalization of a well-studied integration operator acting on the family of Hardy spaces in the unit disc. We study the boundedness and compactness properties of the operator and finally we use these results to give simple proofs of a result of Rättyä and another result by Cohn and Verbitsky.


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Additional Information

Nikolaos Chalmoukis
Affiliation: Dipartimento di Matematica, Universitá di Bologna, Piazza di Porta S. Donato 5, 40127 Bologna, Italy
Email: nikolaos.chalmoukis2@unibo.it

DOI: https://doi.org/10.1090/proc/15016
Received by editor(s): September 2, 2019
Received by editor(s) in revised form: October 24, 2019
Published electronically: May 8, 2020
Additional Notes: The author was supported by the fellowship INDAM-DP-COFUND-2015 “INdAM Doctoral Programme in Mathematics and/or Applications Cofunded by Marie Sklodowska-Curie Actions”, Grant 713485.
Communicated by: Filippo Bracci
Article copyright: © Copyright 2020 American Mathematical Society