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Embedding of function spaces of variable order of differentiation in function spaces of variable order of integration

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The paper deals with embeddings of function spaces of variable order of differentiation in function spaces of variable order of integration. Here the function spaces of variable order of differentiation are defined by means of pseudodifferential operators.

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References

  1. Edmunds, D. E. and Rákosník, J.: Density of smooth functions in W k,p(x). Proc. R. Soc. Lond. A 437 (1992), 229-236.

    Google Scholar 

  2. Illner R.: A class of L p-bounded pseudodifferential operators. Proc. Amer. Mat. Soc. 51 (1975), 347-355.

    Google Scholar 

  3. Jacob, N. and Leopold, H.-G.: Pseudodifferential operators with variable order of differentiation generating Feller semigroups. Integral Equations and Operator Theory 17 (1994), 151-166.

    Google Scholar 

  4. Kikuchi, K. and Negoro, A.: Pseudodifferential operators and Sobolev spaces of variable order of differentiation. Rep. Fac. Liberal Arts, Shizuoka University, Sciences, 31 (1995), 19-27.

    Google Scholar 

  5. Kováčik, O. and Rákosník, J.: On spaces L p(x) and W k,p(x). Czechoslovak Math. J. 41 (1991), 592-618.

    Google Scholar 

  6. Kumano-go, H.: Pseudo-Differential Operators. Massachusetts Institute of Technology Press, Cambridge (Massachusetts)-London, 1981.

    Google Scholar 

  7. Leopold, H.-G.: On Besov spaces of variable order of differentiation. Z. Anal. Anw. 8 (1989), 69-82.

    Google Scholar 

  8. Leopold, H.-G.: On function spaces of variable order of differentiation. Forum Math. 3 (1991), 1-21.

    Google Scholar 

  9. Negoro, A.: Stable-like processes; construction of the transition density and the behavior of sample paths near t = 0. Osaka J. Math. 31 (1994), 189-214.

    Google Scholar 

  10. Samko, S. G.: Differentiation and integration of variable order and the spaces L p(x). Preprint, 1996.

  11. Sharapudinov, I. I.: On a topology of the space L p(t) ([0, 1]). Matem. Zametki 26 (1979), 613-632.

    Google Scholar 

  12. Taylor, M. E.: Pseudodifferential Operators. Princeton University Press, Princeton (New Jersey), 1981.

    Google Scholar 

  13. Triebel, H.: Theory of Function Spaces. Birkhäuser, Basel, 1983.

    Google Scholar 

  14. Tsenov, I. V.: A generalization of the problem of the best approximation in the space L s. Uchen. Zap. Daghestan Gos. Univ 7 (1961), 25-37.

    Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut,Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, D-07743, Jena, Deutschland

    Hans-Gerd Leopold

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  1. Hans-Gerd Leopold
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Leopold, HG. Embedding of function spaces of variable order of differentiation in function spaces of variable order of integration. Czechoslovak Mathematical Journal 49, 633–644 (1999). https://doi.org/10.1023/A:1022483721944

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  • DOI: https://doi.org/10.1023/A:1022483721944

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