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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.
$Hv = {f: Ω → ℂ holomorphic: sup_{z∈ Ω} |f(z)|v(z) < ∞}$
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
19-45
Opis fizyczny
Daty
wydano
2006
Twórcy
autor
- Fakultät für Elektrotechnik, Informatik und Mathematik, Universität Paderborn, Warburger Straße 100, D-33098 Paderborn, Germany
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-1-2