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Hardy spaces of conjugate temperatures

100%

Guzmán-Partida M.

Studia Mathematica

1997

tom 122

nr 2

153-165

We define Hardy spaces of pairs of conjugate temperatures on $ℝ_{+}^{2}$ using the equations introduced by Kochneff and Sagher. As in the holomorphic case, the Hilbert transform relates both components. We demonstrate that the boundary distributions of our Hardy spaces of conjugate temperatures coincide with the boundary distributions of Hardy spaces of holomorphic functions.

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

51%

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

2 Studia Mathematica

2 Guzmán-Partida M.

1 Alvarez J.

1 Skórnik U.

1 2003

1 1997

Wyniki wyszukiwania

Hardy spaces of conjugate temperatures

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