On L₁-subspaces of holomorphic functions

• Autorzy: Anahit Harutyunyan , Wolfgang Lusky
• Języki publikacji: EN

Abstrakty

EN

We study the spaces
$H_{μ}(Ω) = {f: Ω → ℂ holomorphic: ∫_{0}^{R} ∫_{0}^{2π} |f(re^{iφ})| dφdμ(r) < ∞}$
where Ω is a disc with radius R and μ is a given probability measure on [0,R[. We show that, depending on μ, $H_{μ}(Ω)$ is either isomorphic to l₁ or to $(∑ ⊕ Aₙ)_{(1)}$. Here Aₙ is the space of all polynomials of degree ≤ n endowed with the L₁-norm on the unit sphere.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 198
• Numer: 2
• Strony: 157-175

Daty

wydano

2010

Twórcy

autor

Anahit Harutyunyan

• Faculty of Informatics and Applied Mathematics, University of Yerevan, Alek Manukian 1, Yerevan 25, Armenia

autor

Wolfgang Lusky

• Institute of Mathematics, University of Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany

Identyfikatory

DOI

10.4064/sm198-2-4