Extensions of the John-Nirenberg theorem and applications

2019/10/28 by Canto, Javier, Pérez, Carlos · 3 citations
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.12957

Abstract

The John-Nirenberg theorem states that functions of bounded mean oscillation are exponentially integrable. In this article we give two extensions of this theorem. The first one relates the dyadic maximal function to the sharp maximal function of Fefferman-Stein, while the second one concerns local weighted mean oscillations, generalizing a result of Muckenhoupt and Wheeden. Applications to the context of generalized Poincaré type inequalities and to the context of the C_p class of weights are given. Extensions to the case of polynomial BMO type spaces are also given.

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• From generalized Poincaré to Poincaré-Sobolev inequalities via self-improving methods
• Degenerate Poincaré-Sobolev inequalities via fractional integration
• Quantitative BMO-BLO Estimates for the Hardy-Littlewood Maximal Function

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