A version of Gehring lemma in Orlicz spaces

作者：Greco Luigi^*; Zecca Gabriella

来源：Rendiconti Lincei. Matematica e Applicazioni, 2012, 23(1): 29-50.

DOI：10.4171/RLM/615

• Higher integrability
• reverse Holder%26apos
• s inequalities
• mappings of finite distortion

We present a version of the Gehring lemma, showing higher integrability in the scale of Orlicz spaces for a function g satisfying reverse Holder%26apos;s inequalities of the type %26lt;br%26gt;(f(B)g(m))(1/m) %26lt;= f(2B)fg + (f(2B)h(m))(1/m), %26lt;br%26gt;under suitable integrability conditions on f which do not imply boundedness. We describe explicitly in the general case how the improved integrability of g depends on the assumptions on f, thus extending results of [4, 2] which deal with f exponentially integrable. %26lt;br%26gt;We also present some applications of our result to the theory of mappings of finite inner distortion.

• 出版日期2012