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1993 | 64 | 2 | 303-314
Tytuł artykułu

Tame $L^p$-multipliers

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We call an $L^{p}$-multiplier m tame if for each complex homomorphism χ acting on the space of $L^{p}$ multipliers there is some $γ_{0} ∈ Γ$ and |a| ≤ 1 such that $χ(γm) = am(γ_{0}γ)$ for all γ ∈ Γ. Examples of tame multipliers include tame measures and one-sided Riesz products. Tame multipliers show an interesting similarity to measures. Indeed we show that the only tame idempotent multipliers are measures. We obtain quantitative estimates on the size of $L^{p}$-improving tame multipliers which are similar to those obtained for measures, but are false for non-tame multipliers. One-sided Riesz products are seen to play a similar role in the study of tame multipliers as Riesz products do in the study of measures.
Słowa kluczowe
Rocznik
Tom
64
Numer
2
Strony
303-314
Opis fizyczny
Daty
wydano
1993
otrzymano
1991-09-18
poprawiono
1992-07-01
Twórcy
  • Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Bibliografia
  • [1] G. Brown, Riesz products and generalized characters, Proc. London Math. Soc. 30 (1975), 209-238.
  • [2] P. J. Cohen, On a conjecture of Littlewood and idempotent measures, Amer. J. Math. 82 (1960), 191-212.
  • [3] J. Diestel and J. Uhl, Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, R.I., 1977.
  • [4] R. E. Edwards, Fourier Series, Vol. 2, Springer, New York 1982.
  • [5] C. Graham, K. Hare and D. Ritter, The size of $L^p$-improving measures, J. Funct. Anal. 84 (1989), 472-495.
  • [6] C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Springer, New York 1979.
  • [7] A. Grothendieck, Critères de compacité dans les espaces fonctionnels généraux, Amer. J. Math. 74 (1952), 168-186.
  • [8] K. Hare, A characterization of $L^p$-improving measures, Proc. Amer. Math. Soc. 102 (1988), 295-299.
  • [9] K. Hare, Arithmetic properties of thin sets, Pacific J. Math. 131 (1988), 143-155.
  • [10] K. Hare, Properties and examples of $(L^p, L^q)$ multipliers, Indiana Univ. Math. J. 38 (1989), 211-227.
  • [11] K. Hare, Union results for thin sets, Glasgow Math. J. 32 (1990), 241-254.
  • [12] K. Hare, The size of $(L^2, L^p)$ multipliers, Colloq. Math. 63 (1992), 249-262.
  • [13] B. Host et F. Parreau, Ensembles de Rajchman et ensembles de continuité, C. R. Acad. Sci. Paris 288 (1979), 899-902.
  • [14] B. Host et F. Parreau, Sur les mesures dont la transformée de Fourier-Stieltjes ne tend pas vers 0 à l'infini, Colloq. Math. 41 (1979), 285-289.
  • [15] I. Klemes, Idempotent multipliers of $H^1(T)$, Canad. J. Math. 39 (1987), 1223-1234.
  • [16] R. Larson, An Introduction to the Theory of Multipliers, Grundlehren Math. Wiss. 175, Springer, New York 1971.
  • [17] J. F. Méla, Mesures ε-idempotentes de norme bornée, Studia Math. 72 (1982), 131-149.
  • [18] D. Oberlin, A convolution property of the Cantor-Lebesgue measure, Colloq. Math. 47 (1982), 113-117.
  • [19] A. Rajchman, Une classe de séries trigonométriques qui convergent presque partout vers zéro, Math. Ann. 101 (1929), 686-700.
  • [20] L. T. Ramsey and B. B. Wells, Jr., Fourier-Stieltjes transforms of strongly continuous measures, Michigan Math. J. 24 (1977), 13-19.
  • [21] C. Rickart, The General Theory of Banach Algebras, Van Nostrand, Princeton 1960.
  • [22] D. Ritter, Most Riesz product measures are $L^p$-improving, Proc. Amer. Math. Soc. 97 (1986), 291-295.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv64i2p303bwm
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