bilateral composition operators on vector-valued hardy spaces

Bilateral composition operators on vector-valued Hardy spaces

Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$‎. ‎We investigate some operator theoretic properties of‎ ‎bilateral composition operator $C_{ph‎, ‎T}‎: ‎f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq‎ ‎+infty$.‎ ‎Compactness and weak compactness of $C_{ph‎, ‎T}$ on $H^p(X)$‎ ‎are characterized an...

Generalized composition operators on weighted Hardy spaces

Composition Operators between Bergman and Hardy Spaces

We study composition operators between weighted Bergman spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Particular choices for the weights yield results on composition operators between the classical unweighted Bergman and Hardy spaces.

Composition Operators on Hardy Spaces on Lavrentiev Domains

For any simply connected domain Ω, we prove that a Littlewood type inequality is necessary for boundedness of composition operators on Hp(Ω), 1 ≤ p < ∞, whenever the symbols are finitely-valent. Moreover, the corresponding “little-oh” condition is also necessary for the compactness. Nevertheless, it is shown that such an inequality is not sufficient for characterizing bounded composition operat...

Composition operators on Hardy-Orlicz spaces on the ball

Compact Weighted Composition Operators and Multiplication Operators between Hardy Spaces