Three Remarks on Carleson Measures for Dirichlet Space

2018/04/22 by Guozheng Cheng, Xiang Fang, Cheng, Guozheng +5
Mathematics · #Advanced Harmonic Analysis Research #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1804.08102

openalex publication_date 2018/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that all doubling measures on the unit disk \mathbbD are Carleson measures for the standard Dirichlet space D. 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.

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