S'-convolvability with the Poisson kernel in the Euclidean case and the product domain case

Josefina Alvarez, Martha Guzmán-Partida, and Urszula Skórnik. "S'-convolvability with the Poisson kernel in the Euclidean case and the product domain case." Studia Mathematica 156.2 (2003): 143-163. <http://eudml.org/doc/284673>.

@article{JosefinaAlvarez2003,
abstract = {We obtain real-variable and complex-variable formulas for the integral of an integrable distribution in the n-dimensional case. These formulas involve specific versions of the Cauchy kernel and the Poisson kernel, namely, the Euclidean version and the product domain version. We interpret the real-variable formulas as integrals of S’-convolutions. We characterize those tempered distribution that are S’-convolvable with the Poisson kernel in the Euclidean case and the product domain case. As an application of our results we prove that every integrable distribution on ℝⁿ has a harmonic extension to the upper half-space $ℝ₊^\{n+1\}$.},
author = {Josefina Alvarez, Martha Guzmán-Partida, Urszula Skórnik},
journal = {Studia Mathematica},
keywords = {-convolution; Poisson kernels; weighted distribution spaces},
language = {eng},
number = {2},
pages = {143-163},
title = {S'-convolvability with the Poisson kernel in the Euclidean case and the product domain case},
url = {http://eudml.org/doc/284673},
volume = {156},
year = {2003},
}

TY - JOUR
AU - Josefina Alvarez
AU - Martha Guzmán-Partida
AU - Urszula Skórnik
TI - S'-convolvability with the Poisson kernel in the Euclidean case and the product domain case
JO - Studia Mathematica
PY - 2003
VL - 156
IS - 2
SP - 143
EP - 163
AB - We obtain real-variable and complex-variable formulas for the integral of an integrable distribution in the n-dimensional case. These formulas involve specific versions of the Cauchy kernel and the Poisson kernel, namely, the Euclidean version and the product domain version. We interpret the real-variable formulas as integrals of S’-convolutions. We characterize those tempered distribution that are S’-convolvable with the Poisson kernel in the Euclidean case and the product domain case. As an application of our results we prove that every integrable distribution on ℝⁿ has a harmonic extension to the upper half-space $ℝ₊^{n+1}$.
LA - eng
KW - -convolution; Poisson kernels; weighted distribution spaces
UR - http://eudml.org/doc/284673
ER -