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Compact differences of composition operators on weighted Dirichlet spaces

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Allen R., Heller K., Pons M.

Open Mathematics

2014

tom 12

nr 7

1040-1051

Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces . Specifically we study differences of composition operators on the Dirichlet space and S 2, the space of analytic functions whose first derivative is in H 2, and then use Calderón’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.

Ograniczanie wyników

1 Open Mathematics

1 Allen R.

1 Heller K.

1 Pons M.

1 2014

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Compact differences of composition operators on weighted Dirichlet spaces