Riemann-Stieltjes operators on Hardy spaces in the unit ball of $\mathbb C^n$

RIEMANN-STIELTJES OPERATORS FROM F(p,q,s) SPACES TO α-BLOCH SPACES ON THE UNIT BALL

Let H(B) denote the space of all holomorphic functions on the unit ball B Cn. We investigate the following integral operators: Tg( f )(z)= ∫ 1 0 f (tz) g(tz)(dt/t), Lg( f )(z)= ∫ 1 0 f (tz)g(tz)(dt/t), f H(B), z B, where g H(B), and h(z)= ∑n j=1 zj(∂h/∂zj)(z) is the radial derivative of h. The operator Tg can be considered as an extension of the Cesàro operator on the unit disk. The boundedness...

Weighted composition operators between weighted Bergman spaces and Hardy spaces on the unit ball of C

In this paper, we study the weighted composition operators Wφ,ψ :f → ψ(f ◦ φ) between weighted Bergman spaces and Hardy spaces on the unit ball of Cn. We characterize the boundedness and the compactness of the weighted composition operators Wφ,ψ :Ap(να)→Aq(νβ) (0 < q < p <∞, −1 < α,β <∞) and Wφ,ψ :Hp(B)→Hq(B) (0 < q < p <∞). © 2006 Elsevier Inc. All rights reserved.

Weighted Composition Operators and Integral-Type Operators between Weighted Hardy Spaces on the Unit Ball

Composition operators on Hardy-Orlicz spaces on the ball

Essential Norms of Weighted Composition Operators between Hardy Spaces in the Unit Ball

Let φ(z) = (φ1(z), · · · , φn(z)) be a holomorphic self-map of Bn and ψ(z) a holomorphic function on Bn, and H(Bn) the class of all holomorphic functions on Bn, where Bn is the unit ball of C , the weight composition operator Wψ,φ is defined by Wψ,φ = ψf(φ) for f ∈ H(Bn). In this paper we estimate the essential norm for the weighted composition operator Wψ,φ acting from the Hardy space H to H (...