Espaces BMO, inégalités de Paley et multiplicateurs idempotents

Hubert Lelièvre

Studia Mathematica (1997)

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


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


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

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 = {},
volume = {123},
year = {1997},

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 -
ER -


  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. 

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.