The Dirichlet problem for the complex Hessian operator in the class $\mathcal{N}_m(Ω,f)$ - El Gasmi, Ayoub (MATHEMATICA SCANDINAVICA, 2021)
Let $Ω\subset \mathbb{C}^{n}$ be a bounded $m$-hyperconvex domain, where $m$ is an integer such that $1≤ m≤ n$. Let $μ$ be a positive Borel measure on $Ω$. We show that if the complex Hessian equation $H_m (u) = μ$ admits a (weak) subsolution in $Ω$, then it admits a (weak) solution with a prescribed least maximal $m$-subharmonic majorant in $Ω$.