Three Remarks on Carleson Measures for Dirichlet Space
Functional Analysis
2018-04-24 v1
Abstract
In this paper, we prove that all doubling measures on the unit disk are Carleson measures for the standard Dirichlet space . The proof has three ingredients. The first one is a characterization of Carleson measures which holds true for general reproducing kernel Hilbert spaces. The second one is another new equivalent condition for Carleson measures, which holds true only for the standard Dirichlet space. The third one is an application of the dyadic method to our settings.
Keywords
Cite
@article{arxiv.1804.08102,
title = {Three Remarks on Carleson Measures for Dirichlet Space},
author = {Guozheng Cheng and Xiang Fang and Zipeng Wang and Jiayang Yu},
journal= {arXiv preprint arXiv:1804.08102},
year = {2018}
}