Embedding and compact embedding between Bergman and Hardy spaces
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909489603543040 |
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| author | Bao, Guanlong Ma, Pan Yan, Fugang Zhu, Kehe |
| author_facet | Bao, Guanlong Ma, Pan Yan, Fugang Zhu, Kehe |
| contents | For Hardy spaces and weighted Bergman spaces on the open unit ball in ${\mathbb C}^n$, we determine exactly when $A^p_α\subset H^q$ or $H^p\subset A^q_α$, where $0<q<\infty$, $0<p<\infty$, and $-\infty<α<\infty$. For each such inclusion we also determine exactly when it is a compact embedding. Although some special cases were known before, we are able to completely cover all possible cases here. We also introduce a new notion called {\it tight fitting} and formulate a conjecture in terms of it, which places several prominent known results about contractive embeddings in the same framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08406 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Embedding and compact embedding between Bergman and Hardy spaces Bao, Guanlong Ma, Pan Yan, Fugang Zhu, Kehe Complex Variables Functional Analysis For Hardy spaces and weighted Bergman spaces on the open unit ball in ${\mathbb C}^n$, we determine exactly when $A^p_α\subset H^q$ or $H^p\subset A^q_α$, where $0<q<\infty$, $0<p<\infty$, and $-\infty<α<\infty$. For each such inclusion we also determine exactly when it is a compact embedding. Although some special cases were known before, we are able to completely cover all possible cases here. We also introduce a new notion called {\it tight fitting} and formulate a conjecture in terms of it, which places several prominent known results about contractive embeddings in the same framework. |
| title | Embedding and compact embedding between Bergman and Hardy spaces |
| topic | Complex Variables Functional Analysis |
| url | https://arxiv.org/abs/2502.08406 |