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Isomorphic Copies of $$\ell ^\infty $$ in the Weighted Hardy Spaces on the Unit Disc by Enrique Alfonso Sánchez-Pérez; Radosław Szwedek is a Mathematics article available to read on EtoBox.

What is Isomorphic Copies of $$\ell ^\infty $$ in the Weighted Hardy Spaces on the Unit Disc about?

Abstract 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 $$H^p$$ 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.

Who reads Isomorphic Copies of $$\ell ^\infty $$ in the Weighted Hardy Spaces on the Unit Disc?

Author

Enrique Alfonso Sánchez-Pérez; Radosław Szwedek

Publisher

Springer Science and Business Media LLC

Published

2023

Language

EN

Field

Mathematics (Physical Sciences)