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Nuclearity of embedding of Sobolev classes to weighted spaces

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References

  1. V. L. Oleinik and B. S. Pavlov, “On boundedness and compactness criteria for certain embedding operators”, in:Problems of Math. Physics, No. 4 (1970), pp. 112–118.

  2. V. G. Maz'ya and T. O. Shaposhnikova,Multipliers in the Spaces of Differentiable Functions [in Russian], Leningrad (1986), p. 403.

  3. E. Sawyer, “Multipliers of Besov and power-weightedL 2-spaces”,Ind. Univ. Math. J.,33, 353–366 (1984).

    Article  MATH  Google Scholar 

  4. A. Pietsch, “r-Nucleare Sobolevsche Eiubettungsoperatoren”, Sammelband “Ellipt. Diff. gleichungen. II”,Schriffenreihe Inst. Math. Akad. Wiss. Berlin, Heft 8, 203–215 (1971).

    Google Scholar 

  5. A. Pietsch,Operator Ideals, VEB Deutscher Verlag der Wissenschaften, Berlin (1978).

    Google Scholar 

  6. I. Stein and G. Weiss,Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, New Jersey (1971).

    MATH  Google Scholar 

  7. A. Tong, “Diagonal nuclear operators inlp-spaces”,Trans. Am. Math. Soc.,143, 233–247 (1969).

    Article  Google Scholar 

  8. E. D. Gluskin, S. V. Kislyakov, and O. I. Reinov, “Tensor products ofp-absolutely summing operators and right (Jp, Up)-multipliers”,Zap. Nauchn. Semin. LOMI,92, 85–102 (1979).

    Google Scholar 

  9. O. G. Parfenov, “Criteria of nuclearity of embedding operators acting between Bergman spaces and weighted Lebesgue spaces”,Math. Nachr.,154, 105–115 (1991).

    Article  MATH  Google Scholar 

  10. O. G. Parfenov, “Properties of embedding operators for some classes of analytic functions”,Algebra Analiz,3, 199–222 (1991).

    MATH  Google Scholar 

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Translated fromZapiski Nauchnykh Seminarov. POMI, Vol. 247, 1997, pp. 156–165.

Translated by S. V. Kislyakov.

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Parfenov, O.G. Nuclearity of embedding of Sobolev classes to weighted spaces. J Math Sci 101, 3139–3145 (2000). https://doi.org/10.1007/BF02673738

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  • DOI: https://doi.org/10.1007/BF02673738

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