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A SIMPLE PROOF OF THE ρ-ADIC VERSION OF THE SOBOLEV EMBEDDING THEOREM

김용철
대한수학회 (The Korean Mathematical Society)|2010.01|대한수학회논문집 (Communications of the KMS)|제25권 제1호|pp. 27-36

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참고문헌

키워드

ρ-adic vector spacethe p-adic Riesz and Bessel potentialSobolev embedding theorem
주제분류수학

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].

Abstract

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].

참고문헌 (8)

  1. Z. I. Borevich, "Number Theory" (1966), Academic press
  2. S. Haran, "Riesz potentials and explicit sums in arithmetic", Invent. Math., 101, pp.697~703 (1990)
  3. ,Analytic potential theory over the p-adics,Ann.Inst.Fourier(Grenoble)43, "Analytic potential theory over the p-adics", Ann. Inst. Fourier(Grenoble), 43(4), pp.905~944 (1993)
  4. Y.-C. Kim, "Carleson measures and the BMO space on the p-adic vector space", Math. Nachr., 282(9), pp.1278~1304 (2009)
  5. E. M. Stein, "Harmonic Analysis; Real variable methods, orthogonality, and oscillatory integrals" (1993), Princeton Univ. Press
  6. M. H. Taibleson, "Fourier Analysis on Local Fields" (1975), Princeton Univ. Press
  7. V. S. Vladimirov, "p-adic quantum mechanics", Commun. Math. Phys., 123, pp.659~676 (1989)
  8. V. S. Vladimirov, "p-adic Analysis and mathematical physics, Series on Soviet & East European Mathematics", World Scientific, I (1992), Singapore

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