JournalsrlmVol. 23, No. 1pp. 29–50

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
A version of Gehring lemma in Orlicz spaces cover
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Abstract

We present a version of the Gehring lemma, showing higher integrability in the scale of Orlicz spaces for a function gg satisfying reverse Hölder's inequalities of the type

(\medintBgm)1/m\medint2Bfg+(\medint2Bhm)1/m,\left(\medint_B g^m\right)^{1/m}\le \medint_{2B}fg+\left(\medint_{2B} h^m\right)^{1/m},

under suitable integrability conditions on ff which do not imply boundedness. We describe explicitly in the general case how the improved integrability of gg depends on the assumptions on ff, thus extending results of [4, 2] which deal with ff 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. 29–50

DOI 10.4171/RLM/615