L ∞ -Khintchine-Bonami inequality in free probability

Artur Buchholz

Banach Center Publications (1998)

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

Abstract

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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.

How to cite

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Buchholz, 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

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  9. [L] M. Leinert, Multiplikatoren diskreter Gruppen, Doctoral Dissertation, University of Heidelberg, 1972. 
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  11. [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. 
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