Embedding theorems and integration operators on Hardy--Carleson type tent spaces induced by doubling weights

Jiale Chen; Bin Liu

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arXiv · 2602.02049

Embedding theorems and integration operators on Hardy--Carleson type tent spaces induced by doubling weights

Jiale Chen·Bin Liu

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Abstract

This paper develops the function and operator theory of Hardy--Carleson--type analytic tent spaces $AT_q^\infty(\omega)$ induced by radial weights $\omega$ satisfying a two-sided doubling condition. We first characterize the positive Borel measures $\mu$ for which the embedding from $AT_p^\infty(\omega)$ into the tent space $T_q^\infty(\mu)$ is bounded for all $0 < p, q < \infty$. A Littlewood--Paley formula for $AT_q^\infty(\omega)$ is then established. Using these results, we give a complete characterization of the boundedness (compactness) of Volterra-type integration operators between $AT_p^\infty(\omega)$ and $AT_q^\infty(\omega)$.

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BibTeX RIS

Jiale Chen, Bin Liu. 2026-02-02. Embedding theorems and integration operators on Hardy--Carleson type tent spaces induced by doubling weights. https://arxiv.org/abs/2602.02049

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