### L^p Estimates for Semi-Degenerate Simplex Multipliers

- Series
- Analysis Seminar
- Time
- Wednesday, September 7, 2016 - 14:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Robert Kesler – 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