JEDNOSTKA NAUKOWA KATEGORII A+

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

Tom 156 / 2003

Josefina Alvarez, Martha Guzmán-Partida, Urszula Skórnik Studia Mathematica 156 (2003), 143-163 MSC: 46F10, 46F05, 46F12. DOI: 10.4064/sm156-2-5

Streszczenie

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 $S^{\prime }$-convolutions. We characterize those tempered distribution that are $S^{\prime }$-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 ${\mathbb R}^{n}$ has a harmonic extension to the upper half-space ${\mathbb R}_{+}^{n+1}$.

Autorzy

  • Josefina AlvarezDepartment of Mathematics
    New Mexico State University
    Las Cruces, NM 88003, U.S.A.
    e-mail
  • Martha Guzmán-PartidaDepartamento de Matemáticas
    Universidad de Sonora
    Hermosillo, Sonora 83000, México
    e-mail
  • Urszula SkórnikWarsaw University of Agriculture
    Nowoursynowska 166
    02-787 Warszawa, Poland
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek