Espaces BMO, inégalités de Paley et multiplicateurs idempotents

Hubert Lelièvre

Studia Mathematica (1997)

  • Volume: 123, Issue: 3, page 249-274
  • ISSN: 0039-3223

Abstract

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Generalizing the classical BMO spaces defined on the unit circle with vector or scalar values, we define the spaces B M O ψ q ( ) and B M O ψ q ( , B ) , where ψ q ( x ) = e x q - 1 for x ≥ 0 and q ∈ [1,∞[, and where B is a Banach space. Note that B M O ψ 1 ( ) = B M O ( ) and B M O ψ 1 ( , B ) = B M O ( , B ) by the John-Nirenberg theorem. Firstly, we study a generalization of the classical Paley inequality and improve the Blasco-Pełczyński theorem in the vector case. Secondly, we compute the idempotent multipliers of B M O ψ q ( ) . Pisier conjectured that the supports of idempotent multipliers of L ψ q ( ) form a Boolean algebra generated by the periodic parts and the finite parts for 2 < q < ∞. We confirm this conjecture with L ψ q ( ) replaced by B M O ψ q ( ) .

How to cite

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Lelièvre, Hubert. "Espaces BMO, inégalités de Paley et multiplicateurs idempotents." Studia Mathematica 123.3 (1997): 249-274. <http://eudml.org/doc/216392>.

@article{Lelièvre1997,
author = {Lelièvre, Hubert},
journal = {Studia Mathematica},
keywords = {bounded mean oscillation; BMO spaces; Paley inequality; Blasco-Pełczyński theorem; idempotent multipliers},
language = {fre},
number = {3},
pages = {249-274},
title = {Espaces BMO, inégalités de Paley et multiplicateurs idempotents},
url = {http://eudml.org/doc/216392},
volume = {123},
year = {1997},
}

TY - JOUR
AU - Lelièvre, Hubert
TI - Espaces BMO, inégalités de Paley et multiplicateurs idempotents
JO - Studia Mathematica
PY - 1997
VL - 123
IS - 3
SP - 249
EP - 274
LA - fre
KW - bounded mean oscillation; BMO spaces; Paley inequality; Blasco-Pełczyński theorem; idempotent multipliers
UR - http://eudml.org/doc/216392
ER -

References

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  1. [BP] O. Blasco and A. Pełczyński, Theorems of Hardy and Paley for vector-valued analytic functions and related classes of Banach spaces, Trans. Amer. Math. Soc. 323 (1991), 335-367. Zbl0744.46039
  2. [CW] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. Zbl0358.30023
  3. [GM] C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Springer, New York, 1979. Zbl0439.43001
  4. [H] H. Helson, Note on harmonic functions, Proc. Amer. Math. Soc. 4 (1953), 686-691. Zbl0052.30203
  5. [Kl] I. Klemes, Idempotent multipliers of H 1 ( T ) , Canad. J. Math. 39 (1987), 1223-1234. Zbl0627.46063
  6. [L] H. Lelièvre, Espaces BMO et multiplicateurs idempotents, thèse de doctorat de l'Université Paris 6, 1995. 
  7. [Pe] A. Pełczyński, Commensurate sequences of characters, Proc. Amer. Math. Soc. 104 (1988), 525-531. Zbl0693.46044
  8. [Pi1] G. Pisier, Les inégalités de Khintchine-Kahane d'après C. Borel, Séminaire sur la géométrie des espaces de Banach 1977-1978, exposé VII, Ecole Polytechnique, Centre de Mathematiques, 1978. 
  9. [Pi2] G. Pisier, De nouvelles caractérisations des ensembles de Sidon, in: Mathematical Analysis and Applications, Part B, Adv. in Math. Suppl. Stud. 7B, Academic Press, 1981, 685-726. Zbl0468.43008
  10. [Pi3] G. Pisier, Factorization of Linear Operators and Geometry of Banach Spaces, CBMS Regional Conf. Ser. in Math. 60, Amer. Math. Soc., 1986. 
  11. [Pi4] G. Pisier, Probabilistic methods in the geometry of Banach spaces, in: Probability and Analysis 1985, Lecture Notes in Math. 1206, Springer, 1996, 167-241. 

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