Harmonic Analysis and Linear Elliptic Equations

摘要本建议分为两部分。在第一部分中，一组问题涉及多参数傅里叶分析，特别是一组关于多线性算子和换向子的问题。目标是尽可能地实现多线性理论和Coifman-Rochberg-Weiss换向子理论。在第二部分中，我们考虑了一组关于非光滑系数的椭圆发散形式或非发散形式算子的问题。该提案涉及分析和偏微分方程一般领域的一系列问题和问题。这些问题的答案将影响任何使用“谐波分析”工具来调查问题的领域的科学探究。事实证明，这些工具在物理科学的各个领域和生命科学的许多领域都是有价值的。

ABSTRACTThis proposal has two parts. In part one, the set of problemsconcerns multiparameter Fourier analysis, and, in particular, a set of questions about multi-linear operators and commutators.The goal is to carry out the multi-linear theory and the Coifman-Rochberg-Weiss commutator theory to the extent possible.In part two, we consider a collection of problems concerningelliptic divergence form or non-divergence form operators withnon-smooth coefficients.The proposal concerns a set of questions and problems in thegeneral area of analysis and partial differential equations.The answers to these questions will impact scientific inquiryin any field which uses tools from "harmonic analysis" to investigate questions. Such tools have proven to be valuablein every area of the physical sciences and in many areasof the life sciences.