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International Journal of Mathematics and Mathematical Sciences
Volume 2014, Article ID 926790, 8 pages
Research Article

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

Department of Mathematics, Inje University, Gimhae 621-749, Gyeongnam, Republic of Korea

Received 11 December 2013; Revised 28 February 2014; Accepted 16 March 2014; Published 9 April 2014

Academic Editor: Shyam L. Kalla

Copyright © 2014 Byung Keun Sohn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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