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We study the bounded and the compact weighted composition operators from theBloch space into the weighted Banach spaces of holomorphic functions on boundedhomogeneous domains, with particular attention to the unit polydisk. Forbounded homogeneous domains, we characterize the bounded weighted compositionoperators and determine the operator norm. In addition, we provide sufficientconditions for compactness. For the unit polydisk, we completely characterizethe compact weighted composition operators, as well as provide computableestimates on the operator norm.

Weighted composition operators from the Bloch space to weighted Banach spaces on bounded homogeneous domains