Isomorphic Copies of ℓ∞ in the Weighted Hardy Spaces on the Unit Disc

It is still unclear whether the density of analytic polynomials in an  H -admissible space is sufficient to the minimality of the space? This question has a purely foundational background, relating fundamental concepts from the theory of H p spaces. We hypothesize that there is no general relationsh...

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Bibliographic Details
Published inThe Journal of fourier analysis and applications Vol. 29; no. 3
Main Authors Sánchez-Pérez, Enrique Alfonso, Szwedek, Radosław
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2023
Springer Nature B.V
Subjects
Abstract Harmonic Analysis
Approximations and Expansions
Density
Fourier Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Partial Differential Equations
Polynomials
Signal,Image and Speech Processing
46E15
46B26
46A16
42B30
46B03
46E30
Hardy spaces
Banach spaces of analytic functions
Nonseparable Banach spaces
Isomorphic theory of Banach spaces
30H10
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Summary:It is still unclear whether the density of analytic polynomials in an  H -admissible space is sufficient to the minimality of the space? This question has a purely foundational background, relating fundamental concepts from the theory of H p spaces. We hypothesize that there is no general relationship between the density of analytic polynomials and the  R -admissibility of an  H -admissible space. We solve this problem by finding suitable counterexamples of Hardy spaces built upon some weighted Lebesgue spaces. In particular, we provide a direct construction of weights from Szegő class, which guarantees the existence of isomorphic copies of the space of bounded sequences in weighted Hardy spaces on the unit disc.
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-023-10012-8