| 概要 |
We discuss smoothing estimates for velocity averages of the
solution to the kinetic transport equation using hyperbolic Sobolev
spaces. The desired estimates will be shown to be equivalent to certain
mixed-norm estimates for a Fourier multiplier operator associated with
the cone. Such multiplier estimates have a tight relationship with
Strichartz estimates for the wave equation. In this talk, we discuss
these connections with an emphasis on a certain critical case. Based on
joint work with Jonathan Bennett, Jayson Cunanan, Susana Gutierrez and
Sanghyuk Lee.
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