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Mleczko, Paweł; Rzeczkowski, Michał

Carleson measures on circular domains and canonical embeddings of Hardy spaces into function lattices. (English) Zbl 1439.46021

Banach J. Math. Anal. 13, No. 4, 864-883 (2019).
Summary: 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.

MSC:

46E15 Banach spaces of continuous, differentiable or analytic functions
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords:

Hardy spaces; rearrangement-invariant spaces; composition operators; Carleson measures
PDFBibTeX XMLCite
\textit{P. Mleczko} and \textit{M. Rzeczkowski}, Banach J. Math. Anal. 13, No. 4, 864--883 (2019; Zbl 1439.46021)
Full Text: DOI Euclid

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