1 results
THE ESSENTIAL NORMS OF COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 97 / Issue 2 / April 2018
- Published online by Cambridge University Press:
- 31 January 2018, pp. 297-307
- Print publication:
- April 2018
-
- Article
-
- You have access
- Export citation
-
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.
