Analysis Seminar: "Poincare and Fractional Inequalities in the Matrix Weight Settings with Applications to PDE"

Abstract: We will discuss fractional integral operators and fractional maximal operators acting on matrix weighted spaces. In the matrix weighted setting we prove analogous results to the work of Muckenhoupt and Wheeden in thscalar case. We will also prove Poincare inequalities in matrix weighted spaces and use these inequalities to prove existence and regularity results for systems of degenerate elliptic equations.  Time permitting we will speak about some two weight bump conditions for the matrix weights.

Organizer: John McCarthy