Reverse Hölder inequalities and approximation spaces (Q5931942)

Gehring's celebrated self-improving property [see \textit{F. W. Gehring}, ``The \(L^p\) integrability of partial derivatives of a quasiconformal mappings'', Acta Math. 130, 265-277 (1973; Zbl 0258.30021)] known as ``Gehring's Lemma'' is developed in a geometry-free context. This approach, which uses the interpolation theory, has many advantages, for example, it makes sense also when the underlying measure is not doubling and the corresponding Hardy-Littlewood maximal operator is not well behaved. NEWLINENEWLINENEWLINEThe authors also show how their general form of Gehring's Lemma follows from a general inverse type reiteration theorem for approximation spaces.