Weighted Composition Operators on Some Weighted Spaces in the Unit Ball

Abstract

LetBnbe the unit ball ofCn,H(Bn)the space of all holomorphic functions inBn. Letu∈H(Bn)andαbe a holomorphic self-map ofBn. Forf∈H(Bn), the weigthed composition operatoruCαis defined by(uCαf)(z)=u(z)f(α(z)),z∈Bn.The boundedness and compactness of the weighted composition operator on some weighted spaces on the unit ball are studied in this paper.

Generalized Weighted Composition Operators From Area Nevanlinna Spaces to Weighted-Type Spaces

“…From 7and (8), it follows that condition (5) Let {z k } be a sequence such that |φ(z k )| → 1 as k → ∞. For any c > 0, set…”

“…In the case of n = 0, D n φ,u is the weighted composition operator uC φ . Weighted composition operators between analytic function spaces have been studied in [3,5,9,10,11,12,13,16,18,20,22,23,26,31,34,37,40,42] (see also related references therein). Xiao studied the compact composition operator on the area Nevanlinna space in [32], and characterized the boundedness and compactness of the composition operator from the area Nevanlinna space to the Bloch space in [33].…”

On a new integral-type operator from the Bloch space to Bloch-type spaces on the unit ball

“…Let ϕ be a holomorphic self-map of B. For f ∈ H(B) the composition operator is defined by C ϕ f (z) = f (ϕ(z)) (see, e.g., the monograph [9] or recent papers [10,18,27,37]). …”

Weighted Composition Operators from F(p, q, s) Spaces to Hμ∞ Spaces

“…where μ is normal on 0, 1 see, e.g., [2][3][4] and dσ is the normalized surface measure on ∂B. For 0 < p < ∞, the Q p space is defined by see 9…”