Sharp weak type estimates for weights in the class $A_{p_1, p_2}$

Details Sharp weak type estimates for weights in the class $A_{p_1, p_2}$ Sharp weak type estimates for weights in the class $A_{p_1, p_2}$

2011-05-24

arxiv.org/abs/1105.4848v1

Mathematics

Classical Analysis and ODEs

Submitted to Revista Matematica Iberoamericana

Scientific paper

We get sharp estimates for the distribution function of nonnegative weights, which satisfy so called $A_{p_1, p_2}$ condition. For particular choices of parameters $p_1$, $p_2$ this condition becomes an $A_p$-condition or Reverse H\"{o}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, which satisfies a Reverse H\"{o}lder condition.

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