The sharp $A_p$ constant for weights in a reverse-Hölder class
Abstract
Description
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.
28 pages
28 pages