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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.09424 |
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Table of 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.