On the isomorphism classes of weighted spaces of harmonic and holomorphic functions

• Autorzy: Wolfgang Lusky
• Języki publikacji: EN

Abstrakty

EN

Let Ω be either the complex plane or the open unit disc. We completely determine the isomorphism classes of
$Hv = {f: Ω → ℂ holomorphic: sup_{z∈ Ω} |f(z)|v(z) < ∞}$
and investigate some isomorphism classes of
$hv = {f: Ω → ℂ harmonic : sup_{z∈ Ω} |f(z)|v(z) < ∞}$
where v is a given radial weight function. Our main results show that, without any further condition on v, there are only two possibilities for Hv, namely either $Hv ∼ l_{∞}$ or $Hv ∼ H_{∞}$, and at least two possibilities for hv, again $hv ∼ l_{∞}$ and $hv ∼ H_{∞}$. We also discuss many new examples of weights.

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: 2006
• Tom: 175
• Numer: 1
• Strony: 19-45

Daty

wydano

2006

Twórcy

autor

Wolfgang Lusky

• Fakultät für Elektrotechnik, Informatik und Mathematik, Universität Paderborn, Warburger Straße 100, D-33098 Paderborn, Germany

Identyfikatory

DOI

10.4064/sm175-1-2