非齐次度量测度空间上的BLO型空间
Spaces of Type BLO on Non-homogeneous Metric Measure Spaces
摘要：
设$({\mathcal X}, d, μ)$是度量测度空间，满足所谓的上加倍条件和几何加倍条件.本文引入了空间${\mathop\mathrm{RBLO}}(μ)$，并证明了它是已知空间${\mathop\mathrm{RBMO}}(μ)$的一个子集.此外，作者建立了空间${\mathop\mathrm{RBLO}}(μ)$的几个有用的特征。作为应用，得到了从$L^\infty(μ)$到${\mathop\mathrm{RBLO}}(μ)$的极大Calderón-Zygmund算子的有界性.
英文摘要：
Let $({\mathcal X}, d, μ)$ be a metric measure space and satisfy the so-called upper doubling condition and the geometrically doubling condition. In this paper, the authors introduce the space ${\mathop\mathrm{RBLO}}(μ)$ and prove that it is a subset of the known space ${\mathop\mathrm{RBMO}}(μ)$ in this context. Moreover, the authors establish several useful characterizations for the space ${\mathop\mathrm{RBLO}}(μ)$. As an application, the authors obtain the boundedness of the maximal Calderón-Zygmund operators from $L^\infty(μ)$ to ${\mathop\mathrm{RBLO}}(μ)$.
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