A note for Carleson measure on bounded C-convex domains

Mingjin Li; Jianren Long; Lang Wang

doi:10.48550/arxiv.2512.15158

December 17, 2025Open Access

A note for Carleson measure on bounded C-convex domains

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Key Points

To establish characterizations for boundedness of Carleson embedding on bounded C-convex domains and its equivalence to compactness.
Analyzed Carleson measure in the context of bounded C-convex domains.
Established equivalences related to the boundedness of the Carleson embedding.
Focused on the embedding from A_α^p to L^q(μ) on the domain Ω.
Identified multiple characterizations for boundedness of Carleson embedding.
Demonstrated that boundedness is equivalent to compactness under the sharp B condition.

Implication

Mathematical analysis reveals equivalence of boundedness and compactness of Carleson embedding in complex domains.

Abstract

Let \(0<q<p<∞\), \(Ω\) be a bounded \(\)-convex domains in \(^n\). We establish several equivalent characterizations for the boundedness of Carleson embedding \(J_μ:A_α^p L^q(μ)\) on \(Ω\) with sharp \(\) condition. Furthermore, we prove that the boundedness of \(J_μ\) is equivalent to its compactness.

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Cite This Study

Li et al. (2025) studied this question.

synapsesocial.com/papers/69488bc877063b71e748ce47 https://doi.org/10.48550/arxiv.2512.15158

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A note for Carleson measure on bounded C-convex domains

Key Points

Implication

Abstract

Discussion

Cite This Study

A note for Carleson measure on bounded C-convex domains

Key Points

Implication

Abstract

Discussion

Cite This Study

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