MÖBIUS INVARIANT FUNCTION SPACES and DIRICHLET SPACES with SUPERHARMONIC WEIGHTS

Guanlong Bao, Javad Mashreghi, Stamatis Pouliasis, Hasi Wulan

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Let Dμ be Dirichlet spaces with superharmonic weights induced by positive Borel measures μ on the open unit disk. Denote by M (Dμ) Möbius invariant function spaces generated by Dμ. In this paper, we investigate the relation among Dμ, M (Dμ) 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 (Dμ), under the assumption that the weight function K is concave, we characterize the function K such that QK = BMOA . We also describe inner functions in M (Dμ) spaces.

Original language English 1-18 18 Journal of the Australian Mathematical Society 106 1 https://doi.org/10.1017/S1446788718000022 Published - Feb 1 2019

Keywords

• Dirichlet spaces with superharmonic weights
• Möbius invariant function spaces
• inner functions

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