Holomorphic extension of generalizations of Hp functions

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.

Keywords

• generalization of Hp functions in tube domains
• holomorphic extension
• Fourier-Laplace transform
• edge of the wedge theorem.