An Interpolation Theorem for Sublinear Operators 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 establish an interpolation result that a sublinear operator which is bounded from the Hardy space $H^1(\mu )$ to $L^{1,\infty }(\mu )$ and from $L^{\infty }(\mu )$ to the BMO-type space $\mathrm{RBMO}(\mu )$ is also bounded on $L^p(\mu )$ for all $p\in (1,\infty )$. This extension is not completely straightforward and improves the existing result.

12pages, 0figure

References in corpus (2)

• The Hardy Space $H^1$ on Non-homogeneous Metric Spaces
• Spaces of Type BLO on Non-homogeneous Metric Measure Spaces