Generalized integration operators on Hardy spaces
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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.References
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Additional Information
- Nikolaos Chalmoukis
- Affiliation: Dipartimento di Matematica, Universitá di Bologna, Piazza di Porta S. Donato 5, 40127 Bologna, Italy
- MR Author ID: 1316910
- Email: nikolaos.chalmoukis2@unibo.it
- 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
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 3325-3337
- MSC (2010): Primary 30H10; Secondary 30H35, 47G10
- DOI: https://doi.org/10.1090/proc/15016
- MathSciNet review: 4108841