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Concrete Operators

Ed. by Ross, William / Mashreghi, Javad

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Mathematical Citation Quotient (MCQ) 2017: 0.34

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2299-3282
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Hardy spaces of generalized analytic functions and composition operators

Elodie Pozzi
Published Online: 2018-04-28 | DOI: https://doi.org/10.1515/conop-2018-0002

Abstract

We present some recent results on Hardy spaces of generalized analytic functions on D specifying their link with the analytic Hardy spaces. Their definition can be extended to more general domains Ω . We discuss the way to extend such definitions to more general domains that depends on the regularity of the boundary of the domain ∂Ω. The generalization over general domains leads to the study of the invertibility of composition operators between Hardy spaces of generalized analytic functions; at the end of the paper, we discuss invertibility and Fredholm property of the composition operator C on Hardy spaces of generalized analytic functions on a simply connected Dini-smooth domain for an analytic symbol ∅.

Keywords: Hardy spaces; Generalized analyticity; Composition operators

MSC 2010: 30H10; 47B33; 30C62

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About the article

Received: 2017-03-15

Accepted: 2018-03-01

Published Online: 2018-04-28


Citation Information: Concrete Operators, Volume 5, Issue 1, Pages 9–23, ISSN (Online) 2299-3282, DOI: https://doi.org/10.1515/conop-2018-0002.

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© 2018, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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