Spaces of type BLO on non-homogeneous metric measure

Abstract

Let \left(,d,\mu \right) be a metric measure space satisfying the so-called upper doubling condition and the geometrically doubling condition. In this paper, we introduce the space RBLO(μ) and prove that it is a subset of the known space RBMO(μ) in this context. Moreover, we establish several useful characterizations for the space RBLO(μ). As an application, we obtain the boundedness of the maximal Calderón-Zygmund operators from L^{\infty }\left(\mu \right) to RBLO(μ).

Keywords

Upper doubling / geometrically doubling / RBLO(μ) / maximal operator / Calderón-Zygmund maximal operator

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