Titlebook: Sobolev Spaces in Mathematics I; Sobolev Type Inequal Vladimir Maz’ya Book 2009 Springer-Verlag New York 2009 Sobolev inequlaity.Sobolev i

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Sobolev Embeddings and Hardy Operators, reduced to analogous problems on the generalized ridge (a tree in general). The latter problems involve Hardy type operators on trees with weights depending on geometric properties of the original GRD. Approximation and other singular numbers of Hardy type operators, including global bounds and asy

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Optimality of Function Spaces in Sobolev Embeddings,apply methods of interpolation theory..It is a great honor for me to contribute to this volume dedicated to the centenary of S.L. Sobolev, one of the greatest analysts of the XXth century. The paper concerns a topic belonging to an area bearing the name, called traditionally Sobolev inequalities or

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Cocompact Imbeddings and Structure of Weakly Convergent Sequences,tionals. We give a functional-analytic formulation for the method in a Banach space. The key object is a dislocation space, i.e., a triple (.), where . is a convex functional defining a norm on a Banach space . and . is a group of isometries on .. Bounded sequences in dislocation spaces admit a deco

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,Inequalities of Hardy–Sobolev Type in Carnot–Carathéodory Spaces,al weight, i.e., a nonnegative locally integrable function on Ω, and 1 < . < +∞. Under sharp geometric assumptions on the domain Ω C R. that can be measured equivalently in terms of subelliptic capacities or Hausdorff contents, we establish various forms of Hardy-Sobolev type inequalities.

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Quantitative Sobolev and Hardy Inequalities, and Related Symmetrization Principles, of extremals, and with analogues for Hardy inequalities, where extremals do not exist, but can be replaced by “virtual” extremals. An account of the stability of isoperimetric and symmetrization inequalities, on which these Sobolev and Hardy inequalities rely, is provided as well.

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978-1-4419-2757-6Springer-Verlag New York 2009