Hytönen, Tuomas A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa. (English) Zbl 1246.30087 Publ. Mat., Barc. 54, No. 2, 485-504 (2010). Summary: A new class of metric measure spaces is introduced and studied. This class generalises the well-established doubling metric measure spaces as well as the spaces \((\mathbb{R}^n,\mu)\) with \(\mu(B(x,r))\leq Cr^d\), in which non-doubling harmonic analysis has recently been developed. It seems to be a promising framework for an abstract extension of this theory. Tolsa’s space of regularised BMO functions is defined in this new setting, and the John-Nirenberg inequality is proven. Cited in 18 ReviewsCited in 94 Documents MSC: 30L99 Analysis on metric spaces 42B35 Function spaces arising in harmonic analysis 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) Keywords:non-doubling measure; doubling balls; John-Nirenberg inequality PDFBibTeX XMLCite \textit{T. Hytönen}, Publ. Mat., Barc. 54, No. 2, 485--504 (2010; Zbl 1246.30087) Full Text: DOI arXiv Euclid