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

Abstract

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).