The Dirichlet problem for the complex Hessian operator in the class N_m(Ω,f) - El Gasmi, Ayoub (MATHEMATICA SCANDINAVICA, 2021)
Let ΩC^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.