A new type of bmo space for non-doubling measures
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916435308052480 |
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| author | Li, Shining Zhao, Haijing Li, Baode |
| author_facet | Li, Shining Zhao, Haijing Li, Baode |
| contents | Let $μ$ be a Radon measure on $\mathbb R^{d}$ which may be non-doubling and only satisfies $μ(Q(x,l))\le C_{0}l^{n}$} for all $x\in \mathbb R^{d}$, $l(Q)>0$, with some fixed constants $C_{0}>0$ and $n\in (0,d]$. We introduce a new type of $bmo(μ)$ space which looks bigger than the $rbmo(μ)$ space of Dachun Yang (JAMS,\,2005). And its four equivalent norms are established by constructing some special types of auxiliary doubling cubes. Then we further obtain that this new $rbmo(μ)$ space actually coincides with the $rbmo(μ)$ space of Dachun Yang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09424 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new type of bmo space for non-doubling measures Li, Shining Zhao, Haijing Li, Baode Classical Analysis and ODEs Let $μ$ be a Radon measure on $\mathbb R^{d}$ which may be non-doubling and only satisfies $μ(Q(x,l))\le C_{0}l^{n}$} for all $x\in \mathbb R^{d}$, $l(Q)>0$, with some fixed constants $C_{0}>0$ and $n\in (0,d]$. We introduce a new type of $bmo(μ)$ space which looks bigger than the $rbmo(μ)$ space of Dachun Yang (JAMS,\,2005). And its four equivalent norms are established by constructing some special types of auxiliary doubling cubes. Then we further obtain that this new $rbmo(μ)$ space actually coincides with the $rbmo(μ)$ space of Dachun Yang. |
| title | A new type of bmo space for non-doubling measures |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2410.09424 |