Hardy and BMO spaces on Weyl chambers
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913191979646976 |
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| author | Plewa, Paweł Stempak, Krzysztof |
| author_facet | Plewa, Paweł Stempak, Krzysztof |
| contents | Let $W$ be a finite reflection group associated with root system $R$ in $\mathbb R^d$. Let $C_+$ denote a positive Weyl chamber distinguished by a choice of $R_+$, a set of positive roots. We define and investigate Hardy and BMO spaces on $C_+$ in the framework of boundary conditions given by a homomorphism $η\in\mathrm{Hom}(W,\hat{\mathbb{Z}}_2)$ which attaches the $\pm$ signs to the facets of $C_+$. Specialized to orthogonal root systems, atomic decompositions in $H^1_η$ and $h^1_η$ are obtained and the duality problem is also treated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_13533 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hardy and BMO spaces on Weyl chambers Plewa, Paweł Stempak, Krzysztof Classical Analysis and ODEs Functional Analysis Primary 46E30, Secondary 42B30 Let $W$ be a finite reflection group associated with root system $R$ in $\mathbb R^d$. Let $C_+$ denote a positive Weyl chamber distinguished by a choice of $R_+$, a set of positive roots. We define and investigate Hardy and BMO spaces on $C_+$ in the framework of boundary conditions given by a homomorphism $η\in\mathrm{Hom}(W,\hat{\mathbb{Z}}_2)$ which attaches the $\pm$ signs to the facets of $C_+$. Specialized to orthogonal root systems, atomic decompositions in $H^1_η$ and $h^1_η$ are obtained and the duality problem is also treated. |
| title | Hardy and BMO spaces on Weyl chambers |
| topic | Classical Analysis and ODEs Functional Analysis Primary 46E30, Secondary 42B30 |
| url | https://arxiv.org/abs/2304.13533 |