The sharp Ap constant for weights in a reverse-H\"older class
Abstract
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 Ap 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 Ap constants of reverse-H\"older-class weights defined on rectangles and on cubes in n dimensions.
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