Characterizations of Hardy spaces on tube domains over polyhedral cones
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917348883038208 |
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| author | Fu, Zunwei Grafakos, Loukas Wang, Wei Wu, Qingyan |
| author_facet | Fu, Zunwei Grafakos, Loukas Wang, Wei Wu, Qingyan |
| contents | This paper is devoted to the equivalence of various characterizations of holomorphic $H^1$ Hardy spaces on tube domains over polyhedral cones. We establish a new iterated Poisson integral formula which reproduces holomorphic functions on such domains. However, this formula shows that holomorphic $H^1$ functions have boundary values in a new type of Hardy space of real variables on their Shilov boundaries $\mathbb{R}^n$, which cannot be treated by standard classical multi-parameter harmonic analysis. We overcome this difficulty by developing techniques suitably adapted in this setting. Using the iterated Poisson integral as our approximation to the identity, and employing a lifting technique, we introduce various notions of multi-parameter analysis adapted to tube domains, such as twisted rectangles, new non-tangential approach regions, non-tangential maximal functions and Littlewood-Paley type functions. All these notions exhibit new geometric features associated with polyhedral cones and involve hidden parameters, as in the flag setting. We develop the necessary multi-parameter tools to investigate these new Hardy spaces. In particular, we apply these tools to obtain equivalent characterizations of the holomorphic $H^1$ Hardy spaces on tube domains in terms of non-tangential maximal, Lusin-Littlewood-Paley area and Littlewood-Paley $g$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16097 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterizations of Hardy spaces on tube domains over polyhedral cones Fu, Zunwei Grafakos, Loukas Wang, Wei Wu, Qingyan Complex Variables Functional Analysis 42B30, 42B35, 42B25, 32A35 This paper is devoted to the equivalence of various characterizations of holomorphic $H^1$ Hardy spaces on tube domains over polyhedral cones. We establish a new iterated Poisson integral formula which reproduces holomorphic functions on such domains. However, this formula shows that holomorphic $H^1$ functions have boundary values in a new type of Hardy space of real variables on their Shilov boundaries $\mathbb{R}^n$, which cannot be treated by standard classical multi-parameter harmonic analysis. We overcome this difficulty by developing techniques suitably adapted in this setting. Using the iterated Poisson integral as our approximation to the identity, and employing a lifting technique, we introduce various notions of multi-parameter analysis adapted to tube domains, such as twisted rectangles, new non-tangential approach regions, non-tangential maximal functions and Littlewood-Paley type functions. All these notions exhibit new geometric features associated with polyhedral cones and involve hidden parameters, as in the flag setting. We develop the necessary multi-parameter tools to investigate these new Hardy spaces. In particular, we apply these tools to obtain equivalent characterizations of the holomorphic $H^1$ Hardy spaces on tube domains in terms of non-tangential maximal, Lusin-Littlewood-Paley area and Littlewood-Paley $g$-functions. |
| title | Characterizations of Hardy spaces on tube domains over polyhedral cones |
| topic | Complex Variables Functional Analysis 42B30, 42B35, 42B25, 32A35 |
| url | https://arxiv.org/abs/2603.16097 |