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On the equivalence of the K-functional and moduli of continuity and some applications

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Constructive Theory of Functions of Several Variables

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 571))

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References

  1. Adams, R.A.: Sobolev Spaces, New York 1975.

    Google Scholar 

  2. Besov, O.V.: Inequalities for moduli of continuity of functions defined on a domain and imbedding theorems. Soviet Math.Dokl. 13 (1972), 113–117.

    MATH  Google Scholar 

  3. Bramble, J.H.-Hilbert, S.R.: Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation. SIAM J.Numer.Anal. 7 (1970), 112–114.

    Article  MathSciNet  MATH  Google Scholar 

  4. Brudnyi, Ju.A.: A multidimensional analogue of a theorem of Whitney. Math. USSR Sb. 11 (1970), 157–170.

    Article  MathSciNet  Google Scholar 

  5. Buter, P.L.-Berens, H.: Semigroups of Operators and Approximation. Berlin 1967.

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  6. De Vore, R.: Degree of Approximation. Proceedings of the Symposium on Approximation Theory, Austin 1976 (to appear).

    Google Scholar 

  7. Morrey, C., Multiple integrals in the calculus of variations. New York 1966.

    Google Scholar 

  8. Nikolskii, S.M.: Approximation of Functions of Several Variables and Imbedding Theorems, New York 1975.

    Google Scholar 

  9. Scherer, K.: Bernstein type inequalities in Banach spaces. Math. Notes (Mat. Zametki) 17 (1975), 555–562.

    Article  MathSciNet  MATH  Google Scholar 

  10. Stein, E.M.: Singular Integrals and Differentiability properties of functions. Princeton 1970.

    Google Scholar 

  11. Timan, A.F.: Theory of Approximation of Functions of a Real Variable. New York 1963.

    Google Scholar 

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© 1977 Springer-Verlag Berlin · Heidelberg

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Johnen, H., Scherer, K. (1977). On the equivalence of the K-functional and moduli of continuity and some applications. In: Schempp, W., Zeller, K. (eds) Constructive Theory of Functions of Several Variables. Lecture Notes in Mathematics, vol 571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086569

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  • DOI: https://doi.org/10.1007/BFb0086569

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08069-5

  • Online ISBN: 978-3-540-37496-1

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