The Multiplication Operator from F p , q , s Spaces to n th Weighted - Type Spaces on the Unit Disk

Generalized Weighted Composition Operators From Logarithmic Bloch Type Spaces to $ n $'th Weighted Type Spaces

Let $ mathcal{H}(mathbb{D}) $ denote the space of analytic functions on the open unit disc $mathbb{D}$. For a weight $mu$ and a nonnegative integer $n$, the $n$'th weighted type space $ mathcal{W}_mu ^{(n)} $ is the space of all $fin mathcal{H}(mathbb{D}) $ such that $sup_{zin mathbb{D}}mu(z)left|f^{(n)}(z)right|begin{align*}left|f right|_{mathcal{W}_...

A Note on Weighted Composition Operators on L^p-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...

Definition and Properties of the Libera Operator on Mixed Norm Spaces

We consider the action of the operator ℒg(z) = (1 - z)(-1)∫ z (1)‍f(ζ)dζ on a class of "mixed norm" spaces of analytic functions on the unit disk, X = H α,ν (p,q) , defined by the requirement g ∈ X ⇔ r ↦ (1 - r) (α) M p (r, g ((ν))) ∈ L (q) ([0,1], dr/(1 - r)), where 1 ≤ p ≤ ∞, 0 < q ≤ ∞, α > 0, and ν is a nonnegative integer. This class contains Besov spaces, weighted Bergman spaces, Dirichlet...

Weighted composition operators from Bergman-type spaces into Bloch spaces

Let D be the open unit disk in the complex plane C. Denote by H(D) the class of all functions analytic on D. An analytic self-map φ : D → D induces the composition operator Cφ on H(D), defined by Cφ ( f ) = f (φ(z)) for f analytic on D. It is a well-known consequence of Littlewood’s subordination principle that the composition operator Cφ is bounded on the classical Hardy and Bergman spaces (se...