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Multi-Linear Multipliers Associated to Simplexes of Arbitrary Length

Multi-Linear Multipliers Associated to Simplexes of Arbitrary Length

Chapter:
(p.346) Chapter Fourteen Multi-Linear Multipliers Associated to Simplexes of Arbitrary Length
Source:
Advances in Analysis
Author(s):
Camil MuscaluTerence TaoChristoph Thiele, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691159416.003.0014

This chapter introduces two sets of theorems based on a study of the Littlewood–Paley boundedness properties of a tri-linear operator. It generalizes and proves similar estimates for multi-linear multipliers whose symbols are given by characteristic functions of simplexes of arbitrary length. The chapter introduces the so-called AKNS systems, which play an important role in nuclear physics, and describes their connection with certain operators. Then, the rest of the chapter is devoted to the proof of a third theorem, which has been derived from the first two. To conclude, the chapter also proves the “delicate Bessel” Lemma which plays an important role in the argument.

Keywords:   Littlewood–Paley boundedness, tri-linear operator, multi-linear multipliers, simplexes, AKNS systems, delicate Bessel

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