Estimates of essential norms of weighted composition operators between Bloch-type spaces

We estimate the essential norm of weighted composition operators u C φ acting on Bloch-type spaces  B α in terms of the analytic function u : D → C and the n -th power of the analytic selfmap  φ of the open unit disc  D . We obtain new characterizations for boundedness and compactness of u C φ : B α → B β for all 0 < α , β < ∞ , thus answering an open problem of Manhas and Zhao concerning the case α = 1 .