Mathematical Sciences: Weighted Norm Inequalities and Applications

点击翻译按钮获取中文摘要

Wheeden DMS-9500799 The research will investigate the role of weighted norm inequalities in harmonic analysis and differential equations. The emphasis is to study questions that arise naturally in these subjects, and to obtain conditions on the weights or measures which are as sharp and simple to verify as possible, and which reflect the particular nature of the situation being studied. The problems are related to finding weighted norm estimates between a function and various transforms of the function. Mathematical research in harmonic analysis seeks to study the fine structure of mathematical functions and their underlying domains of definition. The tools developed by this work bring out hidden relationships not ordinarily detected by more classical methods.