L^p Estimates for Semi-Degenerate Simplex Multipliers

Analysis Seminar
Wednesday, September 7, 2016 - 2:05pm
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
Multilinear singular integral operators associated to simplexes arise naturally in the dynamics of AKNS systems. One area of research has been to understand how the choice of simplex affects the estimates for the corresponding operator. In particular, C. Muscalu, T. Tao, C. Thiele have observed that degenerate simplexes yield operators satisfying no L^p estimates, while non-degenerate simplex operators, e.g. the trilinear Biest, satisfy a wide range of L^p estimates provable using time-frequency arguments. In this talk, we shall define so-called semi-degenerate simplex multipliers, which as the terminology suggests, lie somewhere between the degenerate and non-degenerate settings and then introduce new L^p estimates for such objects. These results are known to be sharp with respect to target Lebesgue exponents, unlike the best known Biest estimates, and rely on carefully localized interpolation arguments