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

Abstract

Let Ω be a smoothly bounded convex domain of finite type in ℂ n , ∂Ω be the boundary of Ω, S α (f) and g(f) be the area integral and Littlewood-Paley g-function on ∂Ω, respectively. If f e BMOA, then S α (f) < ∞ a.e. on ∂Ω, and there exists a constant C such that ‖S α (f)‖* ੽ C‖f‖*. The same result also holds for g(f).