# ${L}_{\infty}$-Khintchine-Bonami inequality in free probability

Banach Center Publications (1998)

- Volume: 43, Issue: 1, page 105-109
- ISSN: 0137-6934

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topBuchholz, Artur. "$L_∞$-Khintchine-Bonami inequality in free probability." Banach Center Publications 43.1 (1998): 105-109. <http://eudml.org/doc/208829>.

@article{Buchholz1998,

abstract = {We prove the norm estimates for operator-valued functions on free groups supported on the words with fixed length ($f = ∑_\{|w| = l\} a_\{w\} ⊗ λ(w)$). Next, we replace the translations by the free generators with a free family of operators and prove inequalities of the same type.},

author = {Buchholz, Artur},

journal = {Banach Center Publications},

keywords = {Khintchine inequality; Rademacher functions; -Khintchine-Bonami inequalities; operator-valued functions},

language = {eng},

number = {1},

pages = {105-109},

title = {$L_∞$-Khintchine-Bonami inequality in free probability},

url = {http://eudml.org/doc/208829},

volume = {43},

year = {1998},

}

TY - JOUR

AU - Buchholz, Artur

TI - $L_∞$-Khintchine-Bonami inequality in free probability

JO - Banach Center Publications

PY - 1998

VL - 43

IS - 1

SP - 105

EP - 109

AB - We prove the norm estimates for operator-valued functions on free groups supported on the words with fixed length ($f = ∑_{|w| = l} a_{w} ⊗ λ(w)$). Next, we replace the translations by the free generators with a free family of operators and prove inequalities of the same type.

LA - eng

KW - Khintchine inequality; Rademacher functions; -Khintchine-Bonami inequalities; operator-valued functions

UR - http://eudml.org/doc/208829

ER -

## References

top- [Bo1] M. Bożejko, On Λ(p) sets with minimal constant in discrete noncommutative groups, Proc. Amer. Math. Soc. 51(2) (1975), 407-412. Zbl0321.43004
- [Bo2] M. Bożejko, A q-deformed probability, Nelson's inequality and central limit theorems, Non-linear fields, classical, random, semiclassical, (eds. P. Garbaczewski and Z. Popowicz), World Scientific, Singapore (1991), 312-335.
- [BSp] M. Bożejko and R. Speicher, Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces, Math. Annalen 300 (1994), 97-120. Zbl0819.20043
- [Bn] A. Bonami, Étude des coefficients de Fourier des fonctions de ${L}^{p}\left(G\right)$, Ann. Inst. Fourier 20,2 (1970), 335-402. Zbl0195.42501
- [Bu] A. Buchholz, Norm of convolution by operator-valued functions on free groups, To appear in Proc. Amer. Math. Soc.
- [H1] U. Haagerup, Les meilleures constantes de l'inégalité de Khintchine, C. R. Acad. Soc. Paris 286 (1978), A259-A262. Zbl0377.46013
- [H2] U. Haagerup, An example of a non-nuclear C*-algebra which has the metric approximation property, Invent. Math. 50 (1979), 279-293. Zbl0408.46046
- [HP] U. Haagerup and G. Pisier, Bounded linear operators between C*-algebras, Duke Math. J. 71 (1993), 889-925. Zbl0803.46064
- [L] M. Leinert, Multiplikatoren diskreter Gruppen, Doctoral Dissertation, University of Heidelberg, 1972.
- [LPP] F. Lust-Piquard and G. Pisier, Non commutative Khintchine and Paley inequalities, Ark. Mat. 29 (1991), 241-260. Zbl0755.47029
- [V] D. Voiculescu, Symmetries of some reduced free product C*-algebras, in: Operator Algebras and Ergodic Theory, Lecture Notes in Math. 1132 (1985), 556-588.
- [VDN] D. Voiculescu, K. Dykema and A. Nica, Free Random Variables, AMS (1992).

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