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

Abstract EN

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.