Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions of Lp-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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2014/926790 |
| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |