The limit class of Gehring type G∞ in the n-dimensional case

Abstract

We consider a class of functions verifying a limit case of Gehring inequalities and we state a propagation theorem that extends a previous result of the authors to the n-dimensional case. A crucial property to get this extension is a characterization of the functions in terms of Chebychev reverse inequalities; the main tool for obtaining this characterization is a covering lemma stated by Bojarski, Sbordone and Wik in [3].

Keywords

• reverse hölder inequality
• muckenhoupt weight
• chebychev inequality