Espaces BMO, inégalités de Paley et multiplicateurs idempotents

Lelièvre, Hubert

Studia Mathematica, Tome 122 (1997), p. 249-274 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $B M O_{ψ_{q}} ()$ .

Publié le : 1997-01-01

Zbl 0890.42003

EUDML-ID : urn:eudml:doc:216392

@article{bwmeta1.element.bwnjournal-article-smv123i3p249bwm,
     author = {Hubert Leli\`evre},
     title = {Espaces BMO, in\'egalit\'es de Paley et multiplicateurs idempotents},
     journal = {Studia Mathematica},
     volume = {122},
     year = {1997},
     pages = {249-274},
     zbl = {0890.42003},
     language = {fra},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv123i3p249bwm}
}

Lelièvre, Hubert. Espaces BMO, inégalités de Paley et multiplicateurs idempotents. Studia Mathematica, Tome 122 (1997) pp. 249-274. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv123i3p249bwm/

Bibliographie

[00000] [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. | Zbl 0744.46039

[00001] [CW] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. | Zbl 0358.30023

[00002] [GM] C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Springer, New York, 1979. | Zbl 0439.43001

[00003] [H] H. Helson, Note on harmonic functions, Proc. Amer. Math. Soc. 4 (1953), 686-691. | Zbl 0052.30203

[00004] [Kl] I. Klemes, Idempotent multipliers of $H^{1} (T)$ , Canad. J. Math. 39 (1987), 1223-1234. | Zbl 0627.46063

[00005] [L] H. Lelièvre, Espaces BMO et multiplicateurs idempotents, thèse de doctorat de l'Université Paris 6, 1995.

[00006] [Pe] A. Pełczyński, Commensurate sequences of characters, Proc. Amer. Math. Soc. 104 (1988), 525-531. | Zbl 0693.46044

[00007] [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.

[00008] [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. | Zbl 0468.43008

[00009] [Pi3] G. Pisier, Factorization of Linear Operators and Geometry of Banach Spaces, CBMS Regional Conf. Ser. in Math. 60, Amer. Math. Soc., 1986.

[00010] [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.