Abstract:In this paper, we give a complete characterization of Bloch--Carleson measures on the unit disc. More precisely, for a finite positive Borel measure $\mu$ on $\mathbb D$, we characterize the boundedness and compactness of the embedding $$
\operatorname{id}:\mathcal B \longrightarrow L^2(\mu) $$ in terms of a dyadic capacity condition associated with $\mu$. The proof is based on the Bergman projection representation of Bloch functions and a dyadic discretization of the corresponding kernel operator. This work further develops the dyadic approach introduced in our recent work on composition operators on $\mathcal Q_p$ spaces, but in a different setting where the embedding involves recovering function values from derivative information.
From: Bingyang Hu [view email]
[v1]
Mon, 15 Jun 2026 14:13:18 UTC (16 KB)
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