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Currently displaying 1 – 4 of 4

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Nonlinear potential theory and Sobolev spaces

Hedberg, Lars Inge — 1986

Nonlinear Analysis, Function Spaces and Applications

Non-Linear Potentials and Approximation in the Mean by Analytic Functions.

Lars Inge Hedberg — 1972

Mathematische Zeitschrift

Weighted Mean Approximation in Carathéodory Regions.

Lars Inge Hedberg — 1968

Mathematica Scandinavica

Thin sets in nonlinear potential theory

Lars-Inge Hedberg; Thomas H. Wolff — 1983

Annales de l'institut Fourier

Let $L_{α}^{q} (R^{D}), α > 0, 1 < q < \infty$ , denote the space of Bessel potentials $f = G_{α} * g$ , $g \in L^{q}$ , 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...

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