Convolution inequalities on finite cyclic groups and the pseudomeasure norm
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- by David L. Ritter PDF
- Proc. Amer. Math. Soc. 91 (1984), 589-592 Request permission
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.References
- William Beckner, Inequalities in Fourier analysis, Ann. of Math. (2) 102 (1975), no. 1, 159–182. MR 385456, DOI 10.2307/1970980
- 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
- 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 283496
- Daniel M. Oberlin, A convolution property of the Cantor-Lebesgue measure, Colloq. Math. 47 (1982), no. 1, 113–117. MR 679392, DOI 10.4064/cm-47-1-113-117
- David L. Ritter, Some singular measures on the circle which improve $L^p$ spaces, Colloq. Math. 52 (1987), no. 1, 133–144. MR 891505, DOI 10.4064/cm-52-1-133-144
- David L. Ritter, A convolution theorem for probability measures on finite groups, Illinois J. Math. 28 (1984), no. 3, 472–479. MR 748955
- Elias M. Stein, Harmonic analysis on $R^{n}$, Studies in harmonic analysis (Proc. Conf., DePaul Univ., Chicago, Ill., 1974) MAA Stud. Math., Vol. 13, Math. Assoc. Amer., Washington, D.C., 1976, pp. 97–135. MR 0461002
- Fred B. Weissler, Two-point inequalities, the Hermite semigroup, and the Gauss-Weierstrass semigroup, J. Functional Analysis 32 (1979), no. 1, 102–121. MR 533222, DOI 10.1016/0022-1236(79)90080-6
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 589-592
- MSC: Primary 43A22; Secondary 43A75
- DOI: https://doi.org/10.1090/S0002-9939-1984-0746095-8
- MathSciNet review: 746095