A version of Gehring lemma in Orlicz spaces

  • Luigi Greco

    Università degli Studi di Napoli Federico II, Italy
  • Gabriella Zecca

    Università degli Studi di Napoli Federico II, Italy

Abstract

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.

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. 29–50

DOI 10.4171/RLM/615