Embedding theorems and integration operators on Hardy--Carleson type tent spaces induced by doubling weights
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912868404822016 |
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| author | Chen, Jiale Liu, Bin |
| author_facet | Chen, Jiale Liu, Bin |
| contents | This paper develops the function and operator theory of Hardy--Carleson--type analytic tent spaces $AT_q^\infty(ω)$ induced by radial weights $ω$ satisfying a two-sided doubling condition. We first characterize the positive Borel measures $μ$ for which the embedding from $AT_p^\infty(ω)$ into the tent space $T_q^\infty(μ)$ is bounded for all $0 < p, q < \infty$. A Littlewood--Paley formula for $AT_q^\infty(ω)$ is then established. Using these results, we give a complete characterization of the boundedness (compactness) of Volterra-type integration operators between $AT_p^\infty(ω)$ and $AT_q^\infty(ω)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02049 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Embedding theorems and integration operators on Hardy--Carleson type tent spaces induced by doubling weights Chen, Jiale Liu, Bin Complex Variables 30H99, 42B35, 47G10 This paper develops the function and operator theory of Hardy--Carleson--type analytic tent spaces $AT_q^\infty(ω)$ induced by radial weights $ω$ satisfying a two-sided doubling condition. We first characterize the positive Borel measures $μ$ for which the embedding from $AT_p^\infty(ω)$ into the tent space $T_q^\infty(μ)$ is bounded for all $0 < p, q < \infty$. A Littlewood--Paley formula for $AT_q^\infty(ω)$ is then established. Using these results, we give a complete characterization of the boundedness (compactness) of Volterra-type integration operators between $AT_p^\infty(ω)$ and $AT_q^\infty(ω)$. |
| title | Embedding theorems and integration operators on Hardy--Carleson type tent spaces induced by doubling weights |
| topic | Complex Variables 30H99, 42B35, 47G10 |
| url | https://arxiv.org/abs/2602.02049 |