Abstract

In recent analysis we have defined and studied holomorphic functions in tubes in ℂn which generalize the Hardy Hp functions in tubes. In this paper we consider functions f(z), z=x+iy, which are holomorphic in the tube TC=ℝn+iC, where C is the finite union of open convex cones Cj, j=1,…,m, and which satisfy the norm growth of our new functions. We prove a holomorphic extension theorem in which f(z), z ϵ TC, is shown to be extendable to a function which is holomorphic in T0(C)=ℝn+i0(C), where 0(C) is the convex hull of C, if the distributional boundary values in 𝒮′ of f(z) from each connected component TCj of TC are equal.