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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

international journal of mathematics and mathematical sciences

Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow></mml:math>-Growth

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