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Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

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

Tom 156 / 2003

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
Hermosillo, Sonora 83000, México
e-mail
• Urszula SkórnikWarsaw University of Agriculture
Nowoursynowska 166
02-787 Warszawa, Poland
e-mail

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