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

Wolfgang Lusky

Wolfgang Lusky

Studia Mathematica, Tome 173 (2006), p. 19-45 / Harvested from The Polish Digital Mathematics Library

Résumé

Let Ω be either the complex plane or the open unit disc. We completely determine the isomorphism classes of $H v = f : Ω \to ℂ h o l o m o r p h i c : s u p_{z \in Ω} | f (z) | v (z) < \infty$ and investigate some isomorphism classes of $h v = f : Ω \to ℂ h a r m o n i c : s u p_{z \in Ω} | f (z) | v (z) < \infty$ 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 $H v \sim l_{\infty}$ or $H v \sim H_{\infty}$ , and at least two possibilities for hv, again $h v \sim l_{\infty}$ and $h v \sim H_{\infty}$ . We also discuss many new examples of weights.

Publié le : 2006-01-01

Zbl 1114.46020

EUDML-ID : urn:eudml:doc:285212

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     title = {On the isomorphism classes of weighted spaces of harmonic and holomorphic functions},
     journal = {Studia Mathematica},
     volume = {173},
     year = {2006},
     pages = {19-45},
     zbl = {1114.46020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-1-2}
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Wolfgang Lusky. On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Studia Mathematica, Tome 173 (2006) pp. 19-45. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-1-2/