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

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

2007-09-03

arxiv.org/abs/0709.0243v1

Mathematics

Classical Analysis and ODEs

28 pages

Scientific paper

In a recent paper V. Vasyunin presented a proof of the reverse H\"older 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-H\"older 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-H\"older-class weights defined on rectangles and on cubes in n dimensions.

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