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Composition operators on generalized Bloch spaces of the polydisk

Dana D. Clahane·Stevo Stevic·Zehua Zhou
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Abstract

Let p,q>0. We extend to the n-polydisk previous one-variable characterization results of K. Madigan on the $p$-Lipschitz space and K. Madigan/A. Matheson on the Bloch space by obtaining function-theoretic conditions on a holomorphic self-map of the polydisk such that the induced composition operator is bounded or compact between p- and q-Bloch spaces of the polydisk. These conditions turn out to be different in the cases when p is in (0,1) and when p is at least 1. We also obtain corresponding characterization results for composition operators between generalized little p- and q-Bloch spaces of the polydisk.

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Dana D. Clahane, Stevo Stevic, Zehua Zhou. 2005-07-16. Composition operators on generalized Bloch spaces of the polydisk. https://arxiv.org/abs/math/0507339

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