The sharp A_p constant for weights in a reverse-Hölder class

2007/09/03 by Dindoš, Martin, Wall, Treven · 1 citation
#42B20 #42B25 (Primary) #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.0709.0243

Abstract

In a recent paper V. Vasyunin presented a proof of the reverse Hölder inequality with sharp constants for the weights satisfying the usual Muckenhoupt condition. In this paper we present the inverse, that is, we use the Bellman function technique to find the sharp A_p constants for weights in a reverse-Hölder class on an interval; we also find the sharp constants for the higher-integrability result of Gehring. Additionally, we find bounds for the A_p constants of reverse-Hölder-class weights defined on rectangles and on cubes in n dimensions.

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