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

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