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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2208.06684 |
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| _version_ | 1866909292377931776 |
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| author | Shaabani, Shahaboddin |
| author_facet | Shaabani, Shahaboddin |
| contents | We show that a proper open subset $Ω\subset \mathbb{R}^n$ is an extension domain for $H^p$ ($0<p\le1$), if and only if it satisfies a certain geometric condition. When $n(\frac{1}{p}-1)\in \mathbb{N}$ this condition is equivalent to the global Markov condition for $Ω^c$, for $p=1$ it is stronger, and when $n(\frac{1}{p}-1)\notin \mathbb{N}\cup \{0\}$ every proper open subset is an extension domain for $H^p$. It is shown that in each case a linear extension operator exists. We apply our results to study some complemented subspaces of $BMO(\mathbb{R}^n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_06684 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Extension domains for Hardy spaces Shaabani, Shahaboddin Functional Analysis We show that a proper open subset $Ω\subset \mathbb{R}^n$ is an extension domain for $H^p$ ($0<p\le1$), if and only if it satisfies a certain geometric condition. When $n(\frac{1}{p}-1)\in \mathbb{N}$ this condition is equivalent to the global Markov condition for $Ω^c$, for $p=1$ it is stronger, and when $n(\frac{1}{p}-1)\notin \mathbb{N}\cup \{0\}$ every proper open subset is an extension domain for $H^p$. It is shown that in each case a linear extension operator exists. We apply our results to study some complemented subspaces of $BMO(\mathbb{R}^n)$. |
| title | Extension domains for Hardy spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2208.06684 |