Norm of the evaluation on the vector-valued Hardy space

In this paper, we are concerned with the evaluation Eω on the vector-valued Hardy space Hp(D,H) for a Hilbert space H. We show that for each ω∈D, the evaluation Eω on Hp(D,H) is a bounded linear operator and||Eω||=(11−|ω|2)1pfor1≤p

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2024-03, Vol.531 (1), p.127809, Article 127809
Main Author: Kim, Sumin
Format: Article
Language:English
Subjects:
Evaluation
Hardy spaces
Inner-outer factorization
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Description
Summary:In this paper, we are concerned with the evaluation Eω on the vector-valued Hardy space Hp(D,H) for a Hilbert space H. We show that for each ω∈D, the evaluation Eω on Hp(D,H) is a bounded linear operator and||Eω||=(11−|ω|2)1pfor1≤p
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127809