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arXiv · 2208.03892

Composition-differentiation operators on $S^2(\mathbb{D})$

Robert F. Allen·Katherine Heller·Matthew A. Pons
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Abstract

We investigate composition-differentiation operators acting on the space $S^2$, the space of analytic functions on the open unit disk whose first derivative is in $H^2$. Specifically, we determine characterizations for bounded and compact composition-differentiation operators acting on $S^p$. In addition, for particular classes of inducing maps, we compute the norm, and identify the spectrum. Finally, for particular linear fractional inducing maps, we determine the adjoint of the composition-differentiation operator acting on weighted Bergman spaces which include $S^2, H^2$, and the Dirichlet space.

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BibTeXRIS

Robert F. Allen, Katherine Heller, Matthew A. Pons. 2022-08-08. Composition-differentiation operators on $S^2(\mathbb{D})$. https://arxiv.org/abs/2208.03892

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