Spaces of Type BLO on Non-homogeneous Metric Measure Spaces

Abstract

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

arXiv commentFront. Math. China (to appear)

References in corpus (2)

• The Hardy Space $H^1$ on Non-homogeneous Metric Spaces
• Non-homogeneous Tb theorem and random dyadic cubes on metric measure spaces

Cited by in corpus (5)

• Equivalent boundedness of Marcinkiewicz integrals on non-homogeneous metric measure spaces
• Multilinear fractional integral operators on non-homogeneous metric measure spaces
• Boundedness of fractional integral operators on non-homogeneous metric measure spaces
• Commutators of multilinear singular integral operators on non-homogeneous metric measure spaces
• An Interpolation Theorem for Sublinear Operators on Non-homogeneous Metric Measure Spaces