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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 H v = f : Ω h o l o m o r p h i c : s u p z Ω | f ( z ) | v ( z ) < and investigate some isomorphism classes of h v = f : Ω h a r m o n i c : s u p 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 H v l or H v H , and at least two possibilities for hv, again h v l and h v H . We also discuss many new examples of weights.

On weighted composition operators acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces

Elke Wolf (2011)

Annales Polonici Mathematici

Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator ψ C ϕ acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces. Under some assumptions on the weights we give a characterization for such an operator to be bounded in terms of the weights involved as well as the functions ψ and ϕ

On weighted spaces of functions harmonic in n

Albert I. Petrosyan (2006)

Commentationes Mathematicae Universitatis Carolinae

The paper establishes integral representation formulas in arbitrarily wide Banach spaces b ω p ( n ) of functions harmonic in the whole n .

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