## Title: On a linear Landau equation with the specular reflection boundary condition and the SpSp estimates

**Abstract: **Motivated by studies of the nonlinear kinetic Landau equation in a bounded domain, we investigate the linearized equation with the specular reflection boundary condition. To study the regularity of the solution near the boundary, one needs to develop the SpSp theory (Calderon-Zygmund theory) for the degenerate Kolmogorov-Fokker-Planck equation with `irregular' coefficients in the whole space. This is joint work with Hongjie Dong and Yan Guo. In the second part of the talk, I explain how to derive such SpSp estimates using a `kernel-free' approach. This is joint work with Hongjie Dong.Motivated by studies of the nonlinear kinetic Landau equation in a bounded domain, we investigate the linearized equation with the specular reflection boundary condition. To study the regularity of the solution near the boundary, one needs to develop the SpSp theory (Calderon-Zygmund theory) for the degenerate Kolmogorov-Fokker-Planck equation with `irregular' coefficients in the whole space. This is joint work with Hongjie Dong and Yan Guo. In the second part of the talk, I explain how to derive such SpSp estimates using a `kernel-free' approach.

This is joint work with Hongjie Dong.