Mathematical Sciences: Ap, RHp and Other Weight Conditions

该奖项支持在加权空间调和分析理论中的数学问题方面的博士后工作。AP和RHP权重的理论已经得到了非常详细的发展，但某些估计对这些权重的范数的依赖性还没有得到充分的研究。这项工作将集中于两个具体问题的这种依赖性，一个与算子范数有关，另一个与琼斯分解定理有关。还将进行分析重量条件的工作，这些条件比RHP弱，也不太容易被理解。特别是，将努力寻找涉及RHP权重的结果的WRHp权重的类比。随着时间的允许，还将对Muckenoupt的CP级体重进行进一步的研究。权空间理论的发展是为了理解由微分算子诱导的复积分变换。了解加权积分的比较提供了有关积分如何保持度量或规范的信息。这些数据反过来又说明了微分方程解的存在能够得到保证的程度。

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.