H\"older continuous solutions to complex Hessian equations

We prove the H"older continuity of the solution to complex Hessian equation with the right hand side in $L^p$, $p>\frac{n}{m}$, $1<m<n$, in a $m$-strongly pseudoconvex domain in ${\mathbb{C}}^n$ under some additional conditions on the density near the boundary and on the boundary data.