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- W3147148545 endingPage "611" @default.
- W3147148545 startingPage "584" @default.
- W3147148545 abstract "Given a Banach space X, we consider Hardy spaces of X-valued functions on the infinite polytorus, Hardy spaces of X-valued Dirichlet series (defined as the image of the previous ones by the Bohr transform), and Hardy spaces of X-valued holomorphic functions on l_2 ∩ B_{c0}. The chapter is dedicated to study the interplay between these spaces. It is shown that the space of functions on the polytorus always forms a subspace of the one of holomorphic functions, and these two are isometrically isomorphic if and only if X has ARNP. Then the question arises of what do we find in the side of Dirichlet series when we look at the image of the Hardy space of holomorphic functions. This is also answered, showing that this consists of Dirichlet series for which all horizontal translations (those whose coefficients are (a_n/n^e)) are in mathcal{H}_p with uniformly bounded norms. Also, a version of the brothers Riesz theorem for vector-valued functions is given." @default.
- W3147148545 created "2021-04-13" @default.
- W3147148545 creator A5002208194 @default.
- W3147148545 creator A5027091446 @default.
- W3147148545 creator A5035736049 @default.
- W3147148545 creator A5086529737 @default.
- W3147148545 date "2019-08-08" @default.
- W3147148545 modified "2023-09-23" @default.
- W3147148545 title "Vector-Valued Hardy Spaces" @default.
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