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- Title
THE ESSENTIAL NORMS OF COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES.
- Authors
LI, YUFEI; LU, YUFENG; YU, TAO
- Abstract
Let $\unicode[STIX]{x1D711}$ be an analytic self-map of the unit disc. If $\unicode[STIX]{x1D711}$ is analytic in a neighbourhood of the closed unit disc, we give a precise formula for the essential norm of the composition operator $C_{\unicode[STIX]{x1D711}}$ on the weighted Dirichlet spaces ${\mathcal{D}}_{\unicode[STIX]{x1D6FC}}$ for $\unicode[STIX]{x1D6FC}>0$. We also show that, for a univalent analytic self-map $\unicode[STIX]{x1D711}$ of $\mathbb{D}$, if $\unicode[STIX]{x1D711}$ has an angular derivative at some point of $\unicode[STIX]{x2202}\mathbb{D}$, then the essential norm of $C_{\unicode[STIX]{x1D711}}$ on the Dirichlet space is equal to one.
- Subjects
DIRICHLET forms; MATHEMATICAL forms; CHARACTERS sums (Mathematics); COMPOSITION operators; LINEAR operators
- Publication
Bulletin of the Australian Mathematical Society, 2018, Vol 97, Issue 2, p297
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972717000983