On the Hölder regularity of weighted $m$-subharmonic measures

In this talk, we study the Hölder continuity properties of weighted $m$-subharmonic measure of a compact set $K$ in the class of $m$-subharmonic functions. We prove that if the weighted $m$-subharmonic measure of $K$ is Hölder continuous with respect to $K$ and the weight function also satisfies the Hölder continuity condition on $K$, then it is Hölder continuous everywhere. Similarly, we show that if the above conditions are satisfied for the weighted $m$-Green function of $K$, then it is also Hölder continuous everywhere. This is a joint work with Karim Rakhimov.