Spaces of Type BLO on Non-homogeneous Metric Measure Spaces

Abstract

Let $(\mathcal{X},d,\hat{I}¼)$ 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 $\mathrm{RBLO}(\hat{I}¼)$ and prove that it is a subset of the known space $\mathrm{RBMO}(\hat{I}¼)$ in this context. Moreover, the authors establish several useful characterizations for the space $\mathrm{RBLO}(\hat{I}¼)$. As an application, the authors obtain the boundedness of the maximal Calderón-Zygmund operators from $L^{\infty }(\hat{I}¼)$ to $\mathrm{RBLO}(\hat{I}¼)$.

Front. Math. China (to appear)