Maximum principle in potential theory and imbedding theorems for anisotropic spaces of differentiable functions
Copyright policy )Maximum principle in potential theory and imbedding theorems for anisotropic spaces of differentiable functions
In the first part of the paper some notions of the nonlinear potential theory on homogeneous groups are developed. In particular the generalized maximum principle for some type of kernels is proved. In the second part the maximum principle is used in connection in some imbedding theorems for anisotropic spaces of Bessel and Riesz potentials in \({\mathbb{R}}^ n\) and for Besov spaces. Some estimates for the capacity in those spaces are also given.
homogeneous groups, Bessel potentials, capacity, groups, Potentials and capacities on other spaces, \(L_ p\)-potential theory, imbedding theorems, homogeneous, L\({}_ p\)-potential theory, maximum principle, anisotropic spaces, Riesz potentials, Besov spaces, nonlinear potential theory, Bessel and Riesz potentials, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
homogeneous groups, Bessel potentials, capacity, groups, Potentials and capacities on other spaces, \(L_ p\)-potential theory, imbedding theorems, homogeneous, L\({}_ p\)-potential theory, maximum principle, anisotropic spaces, Riesz potentials, Besov spaces, nonlinear potential theory, Bessel and Riesz potentials, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
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