대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제22권4호
  • /
  • Pages.493-502
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  • 2007
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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SOME ESTIMATES OF LITTLEWOOD-PALEY TYPE OPERATORS IN ARITHMETIC

  • 발행 : 2007.10.31
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초록

We prove that certain square functions of Littlewood-Paley type satisfy certain mapping properties on $L^q(\mathbb{Q}_p^d)$.

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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. Z. I. Borevich and I. R. Shafarevich, Number Theory, 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, submitted
  5. Y.-C. Kim, $L^{q}$ -estimates of maximal operators on the p-adic vector space, preprint
  6. E. M. Stein, Harmonic Analysis; Real variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, 1993
  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. 1, World Scientific, Singapore, 1992