On the Dunford-Pettis Property and Banach Spaces that Contain co.
Let Ω be either the complex plane or the open unit disc. We completely determine the isomorphism classes of and investigate some 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 or , and at least two possibilities for hv, again and . We also discuss many new examples of weights.
We investigate when the trigonometric conjugate to the periodic general Franklin system is a basis in C(𝕋). For this, we find some necessary and some sufficient conditions.
Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator 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
The paper establishes integral representation formulas in arbitrarily wide Banach spaces of functions harmonic in the whole .