Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions of Lp-Growth. (9th April 2014)

• Record Type: Journal Article
• Authors: Sohn, Byung Keun
• Other Names: Kalla Shyam L. Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2014(2014)
• Publication Date: 2014-04-09
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2014/926790
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : Let C be a regular cone in ℝ and let T C = ℝ + i C ⊂ ℂ be a tubular radial domain. Let U be the convolutor in Beurling ultradistributions of L p -growth corresponding to T C . We define the Cauchy and Poisson integral of U and show that the Cauchy integral of U is analytic in T C 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 T C attains U as boundary value in the distributional sense.