Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions ofLp-Growth

Let C be a regular cone in ℝ and let TC=ℝ+iC⊂ℂ be a tubular radial domain. Let U be the convolutor in Beurling ultradistributions of Lp-growth corresponding to TC. We define the Cauchy and Poisson integral of U and show that the Cauchy integral of  U is analytic in TC and satisfies a growth property. We represent  U as the boundary value of a finite sum of suitable analytic functions in tubes by means of the Cauchy integral representation of U. Also we show that the Poisson integral of U corresponding to TC attains U as boundary value in the distributional sense