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The Gehring lemma. (English) Zbl 0888.30017
Duren, Peter (ed.) et al., Quasiconformal mappings and analysis. A collection of papers honoring Frederick W. Gehring to his 70th birthday. Proceedings of the international symposium, Ann Arbor, MI, USA, August 1995. New York, NY: Springer. 181-204 (1998).
Applications and variants of the celebrated Gehring reverse Hölder inequality (the Gehring lemma) [F. W. Gehring, Acta Math. 130, 265-277 (1973; Zbl 0258.30021)] are discussed. These include higher integrability results for the derivatives of the solutions of linear and nonlinear PDE’s and the Gehring lemma in Orlicz spaces. The connection of the Gehring lemma to maximal function inequalities is studied in detail. A useful local reverse Hölder inequality with carefully calculated constants is presented at the end of the paper: this is the inequality which is needed in the local, as well as in the global, estimates for the higher integrability.
For the entire collection see [Zbl 0883.00018].

30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations
42B25 Maximal functions, Littlewood-Paley theory
35D10 Regularity of generalized solutions of PDE (MSC2000)