We present a version of the Gehring lemma, showing higher integrability in the scale of Orlicz spaces for a function satisfying reverse Hölder's inequalities of the type
under suitable integrability conditions on which do not imply boundedness. We describe explicitly in the general case how the improved integrability of depends on the assumptions on , thus extending results of [4, 2] which deal with exponentially integrable.\par We also present some applications of our result to the theory of mappings of finite inner distortion.
Cite this article
Luigi Greco, Gabriella Zecca, A version of Gehring lemma in Orlicz spaces. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 23 (2012), no. 1, pp. 29–50DOI 10.4171/RLM/615