Weighted composition operators between generally weighted Bloch spaces of polydisk

Let ϕ be a holomorphic self-map of the open unit polydisk U ⁿ in C ⁿ and ψ a holomorphic function on U ⁿ , p, q > 0. In this paper, we study the generally weighted Bloch space. The growth estimation of functions in such a kind of space is given by the use of the integral method. Using the growth estimation of functions and the function-theoretical properties of those maps ψ and ϕ, sufficient conditions for the weighted composition operator W _ψ,ϕ induced by ψ and ϕ to be bounded and compact between the generally weighted Bloch spaces are investigated.