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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.16707 |
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| _version_ | 1866914858960683008 |
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| author | Chen, You-Wei Benson |
| author_facet | Chen, You-Wei Benson |
| contents | In this paper we prove that for non-negative measurable functions $f$, \begin{align*} I_αf \in BMO(\mathbb{R}^n) \text{ if and only if } I_αf \in BMO^β(\mathbb{R}^n) \text{ for } β\in (n-α,n]. \end{align*} Here $I_α$ denotes the Riesz potential of order $α$ and $BMO^β$ represents the space of functions of bounded $β$-dimensional mean oscillation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16707 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A self-improving property of Riesz potentials in BMO Chen, You-Wei Benson Functional Analysis In this paper we prove that for non-negative measurable functions $f$, \begin{align*} I_αf \in BMO(\mathbb{R}^n) \text{ if and only if } I_αf \in BMO^β(\mathbb{R}^n) \text{ for } β\in (n-α,n]. \end{align*} Here $I_α$ denotes the Riesz potential of order $α$ and $BMO^β$ represents the space of functions of bounded $β$-dimensional mean oscillation. |
| title | A self-improving property of Riesz potentials in BMO |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2404.16707 |