Generalized Multiplicative Inequalities for Ideal Spaces |
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Authors: | Klimov V S |
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Institution: | (1) Yaroslavl' State University, Russia |
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Abstract: | We study the problem of completely describing the domains that enjoy the generalized multiplicative inequalities of the embedding theorem type. We transfer the assertions for the Sobolev spaces L
p
1() to the function classes that result from the replacement of L
p
() with an ideal space of vector-functions. We prove equivalence of the functional and geometric inequalities between the norms of indicators and the capacities of closed subsets of . The most comprehensible results relate to the case of the rearrangement invariant ideal spaces. |
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Keywords: | multiplicative inequality ideal space domain capacity |
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