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

AbstractWe estimate the essential norm of weighted composition operators uCφ acting on Bloch-type spaces Bα 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 uCφ:Bα→Bβ for all 0<α,β<∞, thus answering an open problem of Manhas and Zhao concerning the case α=1