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Convolution inequalities on finite cyclic groups and the pseudomeasure norm


Author: David L. Ritter
Journal: Proc. Amer. Math. Soc. 91 (1984), 589-592
MSC: Primary 43A22; Secondary 43A75
MathSciNet review: 746095
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Abstract: A characterization of the probability measures that define hypercontractive convolution operators on finite cyclic groups has been given in terms of the pseudomeasure norm. Here the pseudomeasure norm is shown to be a poor quantitative predictor of hypercontractiveness in an asymptotic sense.


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  • [1] William Beckner, Inequalities in Fourier analysis, Ann. of Math. (2) 102 (1975), no. 1, 159–182. MR 0385456
  • [2] William Beckner, Svante Janson, and David Jerison, Convolution inequalities on the circle, Conference on harmonic analysis in honor of Antoni Zygmund, Vol. I, II (Chicago, Ill., 1981) Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983, pp. 32–43. MR 730056
  • [3] Aline Bonami, Étude des coefficients de Fourier des fonctions de 𝐿^{𝑝}(𝐺), Ann. Inst. Fourier (Grenoble) 20 (1970), no. fasc. 2, 335–402 (1971) (French, with English summary). MR 0283496
  • [4] Daniel M. Oberlin, A convolution property of the Cantor-Lebesgue measure, Colloq. Math. 47 (1982), no. 1, 113–117. MR 679392
  • [5] David L. Ritter, Some singular measures on the circle which improve 𝐿^{𝑝} spaces, Colloq. Math. 52 (1987), no. 1, 133–144. MR 891505
  • [6] David L. Ritter, A convolution theorem for probability measures on finite groups, Illinois J. Math. 28 (1984), no. 3, 472–479. MR 748955
  • [7] Elias M. Stein, Harmonic analysis on 𝑅ⁿ, Studies in harmonic analysis (Proc. Conf., DePaul Univ., Chicago, Ill., 1974), Math. Assoc. Amer., Washington, D.C., 1976, pp. 97–135. MAA Stud. Math., Vol. 13. MR 0461002
  • [8] Fred B. Weissler, Two-point inequalities, the Hermite semigroup, and the Gauss-Weierstrass semigroup, J. Funct. Anal. 32 (1979), no. 1, 102–121. MR 533222, 10.1016/0022-1236(79)90080-6

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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0746095-8
Article copyright: © Copyright 1984 American Mathematical Society