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On the Green type kernels on the half space in ℝ n

Masayuki Itô (1978)

Annales de l'institut Fourier

We characterize the Hunt convolution kernels χ on R n ( n ≥ 2 ) whose the Green type kernels on D = { ( x 1 , ... , x n ) ∈ R n ; x 1 > 0 } , V χ : C K ( D ) ∋ f ( χ * f - χ * ...

Thin sets in nonlinear potential theory

Lars-Inge Hedberg, Thomas H. Wolff (1983)

Annales de l'institut Fourier

Let L α q ( R D ) , α > 0 , 1 < q < ∞ , denote the space of Bessel potentials f = G α * g , g ∈ L q , with norm ∥ f ∥ α , q = ∥ g ∥ q . For α integer L α q can be identified with the Sobolev space H α , q .One can associate a potential theory to these spaces much in the same way as classical potential theory is associated to the space H 1 ; 2 , and a considerable part of the theory was carried over to this more general context around 1970. There were difficulties extending the theory of thin sets, however. By means of a new inequality, which characterizes the positive cone in the space...

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