Weighted energy class of $m$-subharmonic functions
In this paper, we introduce the class $\mathcal{E}_{m,F}(Ω)$ and solve complex $m$-Hessian equations in the class $\mathcal{E}_{m,F}(Ω)$. Afterthat, we study subextension in the class $\mathcal{E}_{m,F}(Ω)$ with the weighted Hessian measure of subextension unchanged. This is an extensive version of the result in [24] in the case when the smaller domain is relatively compact inside the large one.
math.CV↗