Carleson-type embeddings with closed range

Konstantin M. Dyakonov

doi:10.48550/arxiv.2505.15079

May 21, 2025Open Access

Carleson-type embeddings with closed range

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Key Points

The study identifies specific carleson measures that lead to closed embedding operators in Hardy spaces.
Findings also extend to (p,q)-carleson measures, offering broader insights into embedding behaviors.
A similar characterization is achieved for embedding operators within the framework of bergman spaces.
Closed range properties are significant for understanding function space embeddings and their applications.

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Implication

This research addresses closed range properties of embedding operators for Carleson measures in Hardy and Bergman spaces.

Abstract

We characterize the Carleson measures $μ$ on the unit disk for which the image of the Hardy space Hᵖ under the corresponding embedding operator is closed in Lᵖ(μ). In fact, a more general result involving $(p,q)$-Carleson measures is obtained. A similar problem is solved in the setting of Bergman spaces.

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Konstantin M. Dyakonov (2025) studied this question.

synapsesocial.com/papers/68f5c338e2d8b12842645970 https://doi.org/10.48550/arxiv.2505.15079

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Carleson-type embeddings with closed range

Key Points

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Implication

Abstract

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Carleson-type embeddings with closed range

Key Points

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Implication

Abstract

Discussion

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