Paper detail

Spaces of Type BLO on Non-homogeneous Metric Measure Spaces

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 ${\mathop\mathrm{RBLO}}(μ)$.