Area integral, Littlewood-Paley g-function and BMOA on convex domains of finite type

Let Omega be a smoothly bounded convex domain of finite type in C(n), ofi be the boundary of Omega , S( alpha )(f) and g(f) be the area integral and Littlewood-Paley g-function on partial differential Omega , respectively. If f member of BMOA, then S( alpha )(f) < infinity a.e. on partial differential Omega , and there exists a constant C such that ||S( alpha )(f)||* less than or equal to C||f||*. The saine resuit also holds for g(f).