DUALITY FOR SOME LARGE SPACES OF ANALYTIC FUNCTIONS
| Autor: | H. Jarchow, J. Xiao, K. J. Wirths, Vicente Montesinos |
|---|---|
| Přispěvatelé: | University of Zurich, Jarchow, H |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
coefficient multipliers nuclear power series spaces General Mathematics Topological tensor product Duality (order theory) Type (model theory) Space (mathematics) Topological vector space 10123 Institute of Mathematics 510 Mathematics weighted Bergman spaces Metrization theorem Interpolation space Dual polyhedron weighted area Nevanlinna classes 2600 General Mathematics Mathematics |
| Popis: | We characterize the duals and biduals of the $L^p$-analogues $\mathcal{N}_\alpha^p$ of the standard Nevanlinna classes $\mathcal{N}_\alpha$, $\alpha\ge-1$ and $1\le p\lt \infty$. We adopt the convention to take $\mathcal{N}_{-1}^p$ to be the classical Smirnov class $\mathcal{N}^+$ for $p=1$, and the Hardy–Orlicz space $LH^p$ $(=(\text{Log}^+H)^p)$ for $1\lt p\lt\infty$. Our results generalize and unify earlier characterizations obtained by Eoff for $\alpha=0$ and $\alpha=-1$, and by Yanigahara for the Smirnov class.Each $\mathcal{N}_\alpha^p$ is a complete metrizable topological vector space (in fact, even an algebra); it fails to be locally bounded and locally convex but admits a separating dual. Its bidual will be identified with a specific nuclear power series space of finite type; this turns out to be the ‘Fréchet envelope’ of $\mathcal{N}_\alpha^p$ as well.The generating sequence of this power series space is of the form $(n^\theta)_{n\in\mathbb{N}}$ for some $0\lt\theta\lt1$. For example, the $\theta$s in the interval $(\smfr12,1)$ correspond in a bijective fashion to the Nevanlinna classes $\mathcal{N}_\alpha$, $\alpha\gt-1$, whereas the $\theta$s in the interval $(0,\smfr12)$ correspond bijectively to the Hardy–Orlicz spaces $LH^p$, $1\lt p\lt \infty$. By the work of Yanagihara, $\theta=\smfr12$ corresponds to $\mathcal{N}^+$.As in the work by Yanagihara, we derive our results from characterizations of coefficient multipliers from $\mathcal{N}_\alpha^p$ into various smaller classical spaces of analytic functions on $\Delta$.AMS 2000 Mathematics subject classification: Primary 46E10; 46A11; 47B38. Secondary 30D55; 46A45; 46E15\vskip-3pt |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|