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Embeddings of anisotropic sobolev spaces

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References

  1. Adams, R. A.: Sobolev spaces. New York, London: Academic Press 1975.

    Google Scholar 

  2. Besov, O. V., V. P. Il'in, & S. N. Nikol'skii: Integral representations of functions and imbedding theorems, I and II. Washington, New York, Toronto, London, Sydney: Winston/Wiley 1978 and 1979.

    Google Scholar 

  3. Birman, M. S., & M. Z. Solomjak: Quantitative analysis in Sobolev embedding theorems and applications to spectral theory, Amer. Math. Soc. Translations 114 (1980).

  4. Borzov, V. V.: On some applications of piecewise polynomial approximations of functions of anisotropic classes W rp , Soviet Math. Dokl. 12 (1971), 804–807.

    Google Scholar 

  5. Borzov, V. V.: Some applications of theorems on piecewise polynomial approximations of functions in anisotropic classes W rp , Problemy Mat. Fiz., vyp. 6, Izdat. Leningrad Univ., Leningrad (1973), 53–67 (Russian).

    Google Scholar 

  6. Carl, B.: Entropy numbers, s-numbers and eigenvalues problem, J. Functional Analysis 41 (1981), 290–306.

    Google Scholar 

  7. Carl, B., & H. Triebel: Inequalities between eigenvalues, entropy numbers and related quantities in Banach spaces, Math. Ann. 251 (1980), 129–133.

    Google Scholar 

  8. Edmunds, D. E.: Embeddings of Sobolev spaces, Proc. Spring School ‘Nonlinear analysis, function spaces and applications’, Teubner-Texte Math. 19 (Teubner, Leipzig 1979), 38–58.

    Google Scholar 

  9. Edmunds, D. E., & R. M. Edmunds: Entropy and approximation numbers of embeddings in Orlicz spaces, J. Lond. Math. Soc. 32 (1985), 528–538.

    Google Scholar 

  10. Edmunds, D. E., & V. B. Moscatelli: Fourier approximation and embeddings of Sobolev spaces, Dissertationes Mathematicae 145 (1977), 1–50.

    Google Scholar 

  11. Fučik, S., o. John, & A. Kufner: Function spaces. Prague: Academia 1977.

    Google Scholar 

  12. König, H.: A formula for the eigenvalues of a compact operator, Studia Math. 65 (1979), 141–146.

    Google Scholar 

  13. König, H.: Some inequalities for the eigenvalues of a compact operator, to appear.

  14. Pietsch, A.: Operator ideals. Berlin: VEB Deutscher Verlag der Wissenschaften 1978.

    Google Scholar 

  15. Stein, E. M.: Singular integrals and differentiability properties of functions. Princeton: Princeton University Press 1970.

    Google Scholar 

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Authors and Affiliations

  1. Mathematics Division, University of Sussex, Sussex

    D. E. Edmunds & R. M. Edmunds

  2. Department of Pure Mathematics, University College, Cardiff

    D. E. Edmunds & R. M. Edmunds

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  1. D. E. Edmunds
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  2. R. M. Edmunds
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Dedicated to Professor James Serrin on the occasion of his 60th birthday

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Edmunds, D.E., Edmunds, R.M. Embeddings of anisotropic sobolev spaces. Arch. Rational Mech. Anal. 94, 245–252 (1986). https://doi.org/10.1007/BF00279865

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  • DOI: https://doi.org/10.1007/BF00279865

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