Year: 2018
Type: preprint
Abstract: In this paper, we prove that all doubling measures on the unit disk $\mathbb{D}$ are Carleson measures for the standard Dirichlet space $\mathcal{D}$. 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.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2799112643