Weighted composition operators from the logarithmic weighted-type space to the weighted Bergman space in Cn

摘要

Let Ω be a bounded, circular, strictly convex domain in Cn with C2 boundary and H(Ω) the space of all analytic functions on Ω. Let u∈H(Ω) and φ be a holomorphic self-map of Ω. The weighted composition operator uCφ on H(Ω) is defined by (uCφ)(f)(z)=u(z)f(φ(z)), where f∈H(Ω) and z∈Ω. Let Hlogγβ(Ω),β>0,γ∈R+, be the logarithmic weighted-type space on Ω, and Aαp(Ω),p∈(0,∞),α∈(-1,∞), the weighted Bergman space on Ω. Here we characterize the boundedness and compactness of the weighted composition operator uCφ:Hlogγβ(Ω)→Aαp(Ω).