Weighted Lp-potential theory on homogeneous groups
Copyright policy )Weighted Lp-potential theory on homogeneous groups
This is an original synthesis of two approaches to nonlinear potential theory. For the first, cfr. \textit{V. G. Maz'ya} and \textit{V. P. Khavin} [Usp. Mat. Nauk 27, No. 6(168), 67-138 (1972; Zbl 0247.31010)] and \textit{D. R. Adams} [Trans. Am. Math. Soc. 297, 73-94 (1986; Zbl 0656.31012), and for the second, in the context of homogeneous Lie groups as in the present paper, the author [Mat. Sb. 180, No. 1, 57-77 (1989; Zbl 0695.31009)]. A large part of the present work is devoted to the detailed study of an appropriate notion of weighted capacity and its relation to weighted Hausdorff measure when the potentials involve weighted \(L^ p\)- integrals. There are various applications of this general theory, related to classical analogues, some of which were announced by the author [Inst. Math., Siber. Branch Acad. Sci. SSSR, Novosibirsk, No. 6 (1990)].
weight functions, weighted nonlinear potential of a measure, weighted energy, homogeneous Lie groups, Potential theory on Riemannian manifolds and other spaces, Potentials and capacities on other spaces, weighted Riesz capacity, weighted capacity, \(L^p\)-spaces and other function spaces on groups, semigroups, etc., homogeneous group, weighted Hausdorff measure, Other generalizations (nonlinear potential theory, etc.)
weight functions, weighted nonlinear potential of a measure, weighted energy, homogeneous Lie groups, Potential theory on Riemannian manifolds and other spaces, Potentials and capacities on other spaces, weighted Riesz capacity, weighted capacity, \(L^p\)-spaces and other function spaces on groups, semigroups, etc., homogeneous group, weighted Hausdorff measure, Other generalizations (nonlinear potential theory, etc.)
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