A note for Carleson measure on bounded $\mathbb{C}$-convex domains

Mingjin Li; Jianren Long; Lang Wang

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arXiv · 2512.15158

A note for Carleson measure on bounded $\mathbb{C}$-convex domains

Mingjin Li·Jianren Long·Lang Wang

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Abstract

Let $0<q<p<\infty$, $\Omega$ be a bounded $\bbC$-convex domains in $\bbC^n$. We establish several equivalent characterizations for the boundedness of Carleson embedding $J_\mu:A_\alpha^p\hookrightarrow L^q(\mu)$ on $\Omega$ with sharp $\cB$ condition. Furthermore, we prove that the boundedness of $J_\mu$ is equivalent to its compactness.

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Mingjin Li, Jianren Long, Lang Wang. 2025-12-17. A note for Carleson measure on bounded $\mathbb{C}$-convex domains. https://arxiv.org/abs/2512.15158

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