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On the Sobolev spaces Wk,1(Rn)

Part of the Lecture Notes in Mathematics book series (LNM,volume 992)

Keywords

  • Differential Operator
  • Sobolev Space
  • Convolution Operator
  • Lorentz Space
  • Fourier Multiplier

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References

  1. BONAMI, A. and POORNIMA, S. Some nonmultipliers for Sobolev spaces. Preprint, Orsay (1982).

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  2. BOURGAIN, J. A Hardy inequality in Sobolev spaces. Preprint (1981).

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  3. GANDULFO, A., GARCIA-CUERVA, J. and TAIBLESON, M. Conjugate system characterization of H1: counterexamples for the Euclidean plane and local fields. Bull. Amer. Math. Soc. 82 (1976), 83–85.

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  4. ORNSTEIN, D. A non inequality for differential operators in the L1-norm. Arkiv. Rat. Mech. Anal. 11 (1962), 40–49.

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  5. S. POORNIMA An embedding theorem for the Sobolev space Wk,1. To appear in Bulletin des Sciences Math.

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  6. S. POORNIMA Multipliers of Sobolev spaces. J. Funct. Anal. 45 (1982), 1–28.

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  7. SCHWARTZ, L. Théorie des distributions. Paris, Hermann (1966).

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  8. STEIN, E. M. Singular integrals and differentiability properties of functions. Princeton (1970).

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  9. STEIN, E. M. and WEISS, G. Introduction to Fourier analysis on euclidean spaces. Princeton (1971).

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© 1983 Springer-Verlag

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Poornima, S. (1983). On the Sobolev spaces Wk,1(Rn). In: Mauceri, G., Ricci, F., Weiss, G. (eds) Harmonic Analysis. Lecture Notes in Mathematics, vol 992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069157

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  • DOI: https://doi.org/10.1007/BFb0069157

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12299-9

  • Online ISBN: 978-3-540-39885-1

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