1 results
MÖBIUS INVARIANT FUNCTION SPACES AND DIRICHLET SPACES WITH SUPERHARMONIC WEIGHTS
- Part of
-
- Journal:
- Journal of the Australian Mathematical Society / Volume 106 / Issue 1 / February 2019
- Published online by Cambridge University Press:
- 12 July 2018, pp. 1-18
- Print publication:
- February 2019
-
- Article
-
- You have access
- Export citation
-
Let
${\mathcal{D}}_{\unicode[STIX]{x1D707}}$ be Dirichlet spaces with superharmonic weights induced by positive Borel measures 
$\unicode[STIX]{x1D707}$ on the open unit disk. Denote by 
$M({\mathcal{D}}_{\unicode[STIX]{x1D707}})$ Möbius invariant function spaces generated by 
${\mathcal{D}}_{\unicode[STIX]{x1D707}}$. In this paper, we investigate the relation among 
${\mathcal{D}}_{\unicode[STIX]{x1D707}}$, 
$M({\mathcal{D}}_{\unicode[STIX]{x1D707}})$ and some Möbius invariant function spaces, such as the space 
$BMOA$ of analytic functions on the open unit disk with boundary values of bounded mean oscillation and the Dirichlet space. Applying the relation between 
$BMOA$ and 
$M({\mathcal{D}}_{\unicode[STIX]{x1D707}})$, under the assumption that the weight function 
$K$ is concave, we characterize the function 
$K$ such that 
${\mathcal{Q}}_{K}=BMOA$. We also describe inner functions in 
$M({\mathcal{D}}_{\unicode[STIX]{x1D707}})$ spaces.
