On the boundedness and compactness of extended Ces\`aro composition operators between weighted Bloch-type spaces

Let ψ ∈ H(Bₙ), the space of all holomorphic functions on the unit ball Bₙ of Cⁿ, φ = (φ₁, …, φₙ) ∈ S(Bₙ) the set of holomorphic self-maps of Bₙ. Let Cψ, φ: Bν (and Bν,0) → Bμ (and Bμ,0) be weighted extended Cesàro operators induced by products of the extended Cesàro operator C_φ and integral operator T_ψ. In this paper, we characterize the boundedness and compactness of Cψ,φ via the estimates for either |φ| or |φₖ| for some k∈ \1,…,n\. At the same time, we also give the asymptotic estimates of the norms of these operators.