Weighted $m$-subharmonic measures

In this talk, we study weighted $m$-subharmonic measures within the class of $m$-subharmonic functions. We investigate their fundamental properties and establish several theorems on $(m,\psi,\delta)$-regularity. In particular, we prove that if the weighted $(m,\psi,\delta)$-subharmonic measure is Hölder continuous with respect to a compact set, then it is Hölder continuous in $D$; this result is novel even in the unweighted case. We also introduce the concepts of $(m,\psi,\delta)$-capacity and weighted $\mathcal{P}_{(m,\psi,\delta)}$-capacity and establish their basic properties.