Multilinear Harmonic Analysis
Loukas Grafakos
- 01 Jan 2014
- pp 479-588
TL;DR: In this article, a multilinear analysis of operators that depend linearly on several functions by treating all inputs as variables and not just some as parameters is presented, based on multiple simultaneous decompositions.
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Abstract: Multivariable calculus provides a robust approach into the study of functions of several variables that goes beyond the narrow perspective of studying a single variable by freezing the other ones. Analogously, multilinear analysis focuses on the study of operators that depend linearly on several functions by treating all inputs as variables and not just some as parameters. This study is based on multiple simultaneous decompositions and is naturally more complicated than its linear counterpart, but is also more far-reaching and yields more flexible results.
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