Abstract
Every function of a class L p (G) (G is a domain in R n) may be represented as a sum of the series of step-functions having nonintersecting supports. This representation is ambiguous, but it proves helpful in the technical sense, since step-functions are the “simplest” of summable functions. On the other hand, step-functions are extremal for (T,p)-capacity associated with the identical operator T: Lp(G) → L p (G).
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© 1990 Kluwer Academic Publishers
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Gol’dshtein, V.M., Reshetnyak, Y.G. (1990). Density of Extremal Functions in Sobolev Spaces with First Generalized Derivatives. In: Quasiconformal Mappings and Sobolev Spaces. Mathematics and its Applications (Soviet Series, vol 54. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1922-8_4
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DOI: https://doi.org/10.1007/978-94-009-1922-8_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7358-5
Online ISBN: 978-94-009-1922-8
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