Banach Journal of Mathematical Analysis

Carleson measures on circular domains and canonical embeddings of Hardy spaces into function lattices

Paweł Mleczko and Michał Rzeczkowski

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We study general variants of spaces of holomorphic functions on circular domains on the complex plane. We define Hardy-type spaces generated by Banach function lattices, for which we prove the Carleson theorem. We also analyze canonical embeddings of such spaces into appropriate function lattices. Finally, we study composition operators on Hardy-type spaces on circular domains and characterize order-boundedness of such maps.

Article information

Banach J. Math. Anal., Volume 13, Number 4 (2019), 864-883.

Received: 25 September 2018
Accepted: 28 February 2019
First available in Project Euclid: 9 October 2019

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Zentralblatt MATH identifier

Primary: 46E15: Banach spaces of continuous, differentiable or analytic functions
Secondary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Hardy spaces rearrangement-invariant spaces composition operators Carleson measures


Mleczko, Paweł; Rzeczkowski, Michał. Carleson measures on circular domains and canonical embeddings of Hardy spaces into function lattices. Banach J. Math. Anal. 13 (2019), no. 4, 864--883. doi:10.1215/17358787-2019-0013.

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