Author | Turesson, Bengt Ove. author |
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Title | Nonlinear Potential Theory and Weighted Sobolev Spaces [electronic resource] / by Bengt Ove Turesson |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2000 |
Connect to | http://dx.doi.org/10.1007/BFb0103908 |
Descript | XII, 180 p. online resource |
Introduction -- Preliminaries: Notation and conventions. Basic results concerning weights -- Sobolev spaces: The Sobolev space $Ŵ(mp) w (/Omega)$. The Sobolev space $Ŵ(mp) w (/Omega)$. Hausdorff measures. Isoperimetric inequalities. Some Sobolev type inequalities. Embeddings into L̂q ยต(ร) -- Potential theory: Norm inequalities for fractional integrals and maximal functions. Meyers' Theory for Lp-capacities. Bessel and Riesz capacities. Hausdorff capacities. Variational capacities. Thinness: The case 1< p