Multilinear Harmonic Analysis
Bilinear Hilbert transforms and multilinear restriction.
Multilinear Harmonic Analysis. Bilinear Hilbert transforms and multilinear restriction.
Foundations and canonical references
The standard treatments of multilinear harmonic analysis approach the subject from complementary angles. Grafakos-2014b, Modern Fourier Analysis (2014) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Supporting and adjacent work
A number of supporting contributions sharpen specific aspects of multilinear harmonic analysis or connect it to neighbouring problems. A proof of the bilinear t(1) theorem (Grafakos et al., 2002) contributes to this area as one of the supporting references that inform current practice.
Open methodological questions for multilinear harmonic analysis include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2014Modern Fourier Analysisgrafakos-2014b
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