Mathematical Sciences: Ap, RHp and Other Weight Conditions

该奖项支持博士后工作的数学 加权空间的调和分析理论中的问题。 Ap和RHp权理论得到了很大的发展 细节，但某些估计对规范的依赖性 这些权重尚未得到充分研究。 这项工作将 关注这种依赖性的两个具体问题，一个是关于 操作规范，另一个与琼斯有关 分解定理 工作也将完成分析重量 比RHp弱的条件， 明白 特别是，将努力寻找类似物， 对于涉及RHp权重的结果的WRHp权重。 进一步 Muckenhoupt类Cp权重的研究也将被视为 时间允许的话。 加权空间理论的发展是为了理解 微分算子诱导的复积分变换。 了解加权积分的比较方式可以提供以下信息 积分如何保持度量或范数。 反过来，这些数据， 说明了在何种程度上存在的解决方案的 微分方程可以保证。

This award supports postdoctoral work on mathematical questions in the theory of harmonic analysis of weighted spaces. The theory of Ap and RHp weight has been developed in great detail, but the dependence of certain estimates on the norm of such weights has not been adequately studied. This work will focus on this dependence for two specific questions, one relating to operator norms, and the other relating to the Jones factorization theorem. Work will also be done analyzing weight conditions which are weaker than RHp and also less well understood. In particular, efforts will be made to find analogs for WRHp weights of results involving RHp weights. Further studies of Muckenhoupt's class Cp weight will also be taken up as time permits. The theory of weighted spaces was developed to understand complex integral transforms induced by differential operators. Understanding how weighted integrals compare gives information on how the integrals preserve metrics or norms. This data, in turn, illustrates the extent to which existence of solutions of the differential equations can be guaranteed.