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1993 | 64 | 2 | 233-244
Tytuł artykułu

On vector-valued inequalities for Sidon sets and sets of interpolation

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let E be a Sidon subset of the integers and suppose X is a Banach space. Then Pisier has shown that E-spectral polynomials with values in X behave like Rademacher sums with respect to $L_p$-norms. We consider the situation when X is a quasi-Banach space. For general quasi-Banach spaces we show that a similar result holds if and only if E is a set of interpolation ($I_0$-set). However, for certain special classes of quasi-Banach spaces we are able to prove such a result for larger sets. Thus if X is restricted to be "natural" then the result holds for all Sidon sets. We also consider spaces with plurisubharmonic norms and introduce the class of analytic Sidon sets.
Słowa kluczowe
Rocznik
Tom
64
Numer
2
Strony
233-244
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-03-17
Twórcy
autor
  • Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211, U.S.A.
Bibliografia
  • [1] N. Asmar and S. J. Montgomery-Smith, On the distribution of Sidon series, Ark. Mat., to appear.
  • [2] D. Grow, A class of $I_0$-sets, Colloq. Math. 53 (1987), 111-124.
  • [3] S. Hartman and C. Ryll-Nardzewski, Almost periodic extensions of functions, ibid. 12 (1964), 23-39.
  • [4] S. Hartman and C. Ryll-Nardzewski, Almost periodic extensions of functions, II, ibid. 15 (1966), 79-86.
  • [5] J.-P. Kahane, Ensembles de Ryll-Nardzewski et ensembles de Helson, ibid. 15 (1966), 87-92.
  • [6] N. J. Kalton, Banach envelopes of non-locally convex spaces, Canad. J. Math. 38 (1986), 65-86.
  • [7] N. J. Kalton, Plurisubharmonic functions on quasi-Banach spaces, Studia Math. 84 (1986), 297-324.
  • [8] J.-F. Méla, Sur les ensembles d'interpolation de C. Ryll-Nardzewski et de S. Hartman, ibid. 29 (1968), 167-193.
  • [9] J.-F. Méla, Sur certains ensembles exceptionnels en analyse de Fourier, Ann. Inst. Fourier (Grenoble) 18 (2) (1968), 32-71.
  • [10] J. Mycielski, On a problem of interpolation by periodic functions, Colloq. Math. 8 (1961), 95-97.
  • [11] A. Pełczyński, Commensurate sequences of characters, Proc. Amer. Math. Soc. 104 (1988), 525-531.
  • [12] G. Pisier, Les inégalités de Kahane-Khintchin d'après C. Borell, in: Séminaire sur la géométrie des espaces de Banach, Ecole Polytechnique, Palaiseau, Exposé VII, 1977-78.
  • [13] C. Ryll-Nardzewski, Concerning almost periodic extensions of functions, Colloq. Math. 12 (1964), 235-237.
  • [14] E. Strzelecki, Some theorems on interpolation by periodic functions, ibid. 12 (1964), 239-248.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-cmv64i2p233bwm
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