Harmonic Analysis and Linear Elliptic Equations

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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.