대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제57권5호
  • /
  • Pages.1143-1149
  • /
  • 2020
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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SOBOLEV TRACE INEQUALITY ON Ws,q(ℝn)

  • 투고 : 2019.09.07
  • 심사 : 2020.04.23
  • 발행 : 2020.09.30
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⟨ 이전 논문 다음 논문 ⟩

초록

Sobolev trace inequalities on nonhomogeneous fractional Sobolev spaces are established.

키워드

참고문헌

  1. K. I. Babenko, An inequality in the theory of Fourier integrals, Izv. Akad. Nauk SSSR Ser. Mat. 25 (1961), 531-542 (Russian); translated as Amer. Math. Soc. Transl. Ser. 2 (44) (1962), 115-128.
  2. W. Beckner, Inequalities in Fourier analysis, Ann. of Math. (2) 102 (1975), no. 1, 159-182. https://doi.org/10.2307/1970980
  3. W. Beckner, Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality, Ann. of Math. (2) 138 (1993), no. 1, 213-242. https://doi.org/10.2307/2946638
  4. A. Einav and M. Loss, Sharp trace inequalities for fractional Laplacians, Proc. Amer. Math. Soc. 140 (2012), no. 12, 4209-4216. https://doi.org/10.1090/S0002-9939-2012-11380-2
  5. J. F. Escobar, Sharp constant in a Sobolev trace inequality, Indiana Univ. Math. J. 37 (1988), no. 3, 687-698. https://doi.org/10.1512/iumj.1988.37.37033
  6. H. C. Pak and Y. J. Park, Sharp trace inequalities on fractional Sobolev spaces, Math. Nachr. 284 (2011), no. 5-6, 761-763. https://doi.org/10.1002/mana.200810206
  7. Y. J. Park, The sharp Sobolev trace inequality in a limiting case, Math. Inequal. Appl. 13 (2010), no. 3, 629-633. https://doi.org/10.7153/mia-13-44