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

Wolfgang Lusky
2006 Studia Mathematica  
Let Ω be either the complex plane or the open unit disc. We completely determine the isomorphism classes of 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. 2000 Mathematics Subject Classification: Primary 46E15; Secondary 46B03.
doi:10.4064/sm175-1-2 fatcat:njiovytfc5hd3mszzmhuepln7a