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LOGARITHMIC FRACTIONAL SOBOLEV TRACE INEQUALITIES

  • Received : 2020.04.26
  • Accepted : 2020.05.05
  • Published : 2020.05.15

Abstract

Logarithmic fractional Sobolev trace inequalities are derived as a generalization of the results in [6, 9].

Keywords

References

  1. W. Beckner, Geometric asymptotics and the logarithmic Sobolev inequality, Forum Math., 11 (1999), 105-137. https://doi.org/10.1515/form.11.1.105
  2. O. V. Besov, On traces on a nonsmooth surface of classes of differentiable functions, Trudy Mat. Inst. Steklov, 117 (1972), 11-24.
  3. E. Gagliardo, Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni di n variabili, Rend. Sem. Mat. Univ. Padova, 27 (1957), 284-305.
  4. L. Gross, Logarithmic Sobolev inequalities, Amer. J. Math., 97 (1975), 1061-1083. https://doi.org/10.2307/2373688
  5. F. Jones, Lebesgue integration on Euclidean space, John and Bartlett Publishers, 1993.
  6. H. C. Pak, Sobolev trace inequality on $W^{s,q}(R^n)$, Bull. Korean Math. Soc., To appear.
  7. H. C. Pak and Y. J. Park, Sharp trace inequalities on fractional Sobolev spaces, Mathematische Nachrichten, 284 (2011), 761-763. https://doi.org/10.1002/mana.200810206
  8. Y. J. Park, Logarithmic Sobolev trace ineqality, Proc. Amer. Math. Soc., 132 (2004), 2075-2083. https://doi.org/10.1090/S0002-9939-03-07329-5
  9. Y. J. Park, Derivation of Logarithmic Sobolev Trace Inequalities, Journal of the Chungcheong Math. Soc., 32 (2019), 239-243. https://doi.org/10.14403/JCMS.2019.32.2.239