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arXiv · 2207.12635

Compact differences of composition operators on weighted Dirichlet spaces

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

Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces $\mathcal{D}_\alpha$. Specifically we study differences of composition operators on the Dirichlet space $\mathcal{D}$ and $S^2$, the space of analytic functions whose first derivative is in $H^2$, and then use Calder\'{o}n's complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.

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Robert F. Allen, Katherine Heller, Matthew A. Pons. 2022-07-26. Compact differences of composition operators on weighted Dirichlet spaces. https://doi.org/10.2478/s11533-013-0397-3

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