Inequalities of John—Nirenberg type in doubling spaces
Buckley, Stephen M. (1999) Inequalities of John—Nirenberg type in doubling spaces. Journal d'Analyse Mathématique, 79 (1). pp. 215-240. ISSN 1565-8538
The concept of an H-chain set in a doubling spaceX, which generalizes that of a Hölder domain in Euclidean space, is defined and investigated. We show that every H-chain set is mean porous and that its outer layer has measure bounded by a power of its thickness. As a consequence, we show that a John-Nirenberg type inequality holds on an open subset Ω ofX if, and often only if, Ω is an H-chain set.
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