Seminar:
Analysis
Event time:
Thursday, February 2, 2023 - 4:15pm
Speaker:
Dominique Maldague
Speaker affiliation:
MIT
Event description:
I will present recent work which proves a sharp L^7 square function estimate for the moment curve (t , t^2, t^3) in R^3 using ideas from decoupling theory. In the context of restriction theory, which concerns functions with specialized (curved) Fourier support, this is the only known sharp square function estimate with a non-even L^p exponent (p=7). The basic set-up is to consider a function f with Fourier support in a small neighborhood of the moment curve. Then partition the neighborhood into box-like subsets and form a square function in the Fourier projections of f onto these box-like regions. We will use a combination of recent tools including the “high-low” method and wave envelope estimates to bound f in L^7 by the square function of f in L^7.