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

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Alvarez J., Guzmán-Partida M., Skórnik U.

Studia Mathematica

2003

tom 156

nr 2

143-163

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 $ℝ₊^{n+1}$.

Ograniczanie wyników

1 Studia Mathematica

1 Alvarez J.

1 Guzmán-Partida M.

1 Skórnik U.

1 2003

Wyniki wyszukiwania

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