대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제25권1호
  • /
  • Pages.27-36
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  • 2010
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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A SIMPLE PROOF OF THE p-ADIC VERSION OF THE SOBOLEV EMBEDDING THEOREM

  • 발행 : 2010.01.31
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초록

We give a simple proof of certain mapping properties of the p-adic Riesz potential and Bessel potential, and the p-adic version of the Sobolev embedding theorem obtained in [6].

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참고문헌

  1. Z. I. Borevich and I. R. Shafarevich, Number Theory, Academic press, New York, 1966.
  2. S. Haran, Riesz potentials and explicit sums in arithmetic, Invent. Math. 101 (1990), 697–703. https://doi.org/10.1007/BF01231521
  3. S. Haran, Analytic potential theory over the p-adics, Ann. Inst. Fourier(Grenoble) 43 (1993), no. 4, 905–944. https://doi.org/10.5802/aif.1361
  4. Y.-C. Kim, Carleson measures and the BMO space on the p-adic vector space, Math. Nachr. 282 (2009), no. 9, 1278–1304. https://doi.org/10.1002/mana.200610806
  5. E. M. Stein, Harmonic Analysis; Real variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, 1993.
  6. M. H. Taibleson, Fourier Analysis on Local Fields, Princeton Univ. Press, 1975.
  7. V. S. Vladimirov and I. V. Volovich, p-adic quantum mechanics, Commun. Math. Phys. 123 (1989), 659–676. https://doi.org/10.1007/BF01218590
  8. V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov, p-adic Analysis and mathematical physics, Series on Soviet & East European Mathematics, Vol. I, World Scientific, Singapore, 1992.

피인용 문헌

  1. Hardy-Littlewood-Sobolev Inequalities onp-Adic Central Morrey Spaces vol.2015, 2015, https://doi.org/10.1155/2015/419532
  2. Sobolev Spaces on Locally Compact Abelian Groups: Compact Embeddings and Local Spaces vol.2014, 2014, https://doi.org/10.1155/2014/404738
  3. Commutator of Riesz potential in p-adic generalized Morrey spaces vol.13, pp.3, 2018, https://doi.org/10.1007/s11464-018-0696-x