Carleson measures on planar sets

Zhijian Qiu

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arXiv · 1307.0424

Carleson measures on planar sets

Zhijian Qiu

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Abstract

In this paper, we investigate what are Carleson measures on open subsets in the complex plane. A circular domain is a connected open subset whose boundary consists of finitely many disjoint circles. We call a domain $G$ multi-nicely connected if there exists a circular domain $W$ and a conformal map $ψ$ from $W$ onto $G$ such that $ψ$ is almost univalent with respect the arclength on $\partial W$. We characterize all Carleson measures for those open subsets so that each of their components is multi-nicely connected and harmonic measures of the components are mutually singular. Our results suggest the extend of Carleson measures probably is up to this class of open subsets.

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BibTeX RIS

Zhijian Qiu. 2013-07-01. Carleson measures on planar sets. https://arxiv.org/abs/1307.0424

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