Sharp weak type estimates for weights in the class A_(p1,p2)

摘要

We get sharp estimates for the distribution function of nonnegative weights that satisfy the so-called A_(p1,p2) condition. For particular choices of parameters p1, p2 this condition becomes an A_p-condition or reverse H?lder condition. We also get maximizers for these sharp estimates. We use the Bellman technique and try to carefully present and motivate our tactics. As an illustration of how these results can be used, we deduce the following result: if a weight w is in A_2 then it self-improves to a weight that satisfies a reverse H?lder condition.