A generalized Kahane-Khinchin inequality

S. Favorov

Studia Mathematica (1998)

  • Volume: 130, Issue: 2, page 101-107
  • ISSN: 0039-3223

Abstract

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The inequality ʃ l o g | ∑ a n e 2 π i φ n | d φ 1 … d φ n ≥ C l o g ( ∑ | a n | 2 ) 1 / 2 with an absolute constant C, and similar ones, are extended to the case of a n belonging to an arbitrary normed space X and an arbitrary compact group of unitary operators on X instead of the operators of multiplication by e 2 π i φ .

How to cite

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Favorov, S.. "A generalized Kahane-Khinchin inequality." Studia Mathematica 130.2 (1998): 101-107. <http://eudml.org/doc/216545>.

@article{Favorov1998,
abstract = {The inequality $ʃ log |∑ a_n e^\{2πiφ_n\}|dφ_1…dφ_n ≥ C log(∑|a_n|^2)^\{1/2\}$ with an absolute constant C, and similar ones, are extended to the case of $a_n$ belonging to an arbitrary normed space X and an arbitrary compact group of unitary operators on X instead of the operators of multiplication by $e^\{2πiφ\}$.},
author = {Favorov, S.},
journal = {Studia Mathematica},
language = {eng},
number = {2},
pages = {101-107},
title = {A generalized Kahane-Khinchin inequality},
url = {http://eudml.org/doc/216545},
volume = {130},
year = {1998},
}

TY - JOUR
AU - Favorov, S.
TI - A generalized Kahane-Khinchin inequality
JO - Studia Mathematica
PY - 1998
VL - 130
IS - 2
SP - 101
EP - 107
AB - The inequality $ʃ log |∑ a_n e^{2πiφ_n}|dφ_1…dφ_n ≥ C log(∑|a_n|^2)^{1/2}$ with an absolute constant C, and similar ones, are extended to the case of $a_n$ belonging to an arbitrary normed space X and an arbitrary compact group of unitary operators on X instead of the operators of multiplication by $e^{2πiφ}$.
LA - eng
UR - http://eudml.org/doc/216545
ER -

References

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  1. [1] S. Yu. Favorov, The distribution of values of holomorphic mappings of ℂ n into Banach space, Funktsional. Anal. i Prilozhen. 21 (1987), no. 3, 91-92 (in Russian); English transl.: Functional Anal. Appl. 21 (1987), 251-252. 
  2. [2] S. Yu. Favorov, Growth and distribution of values of holomorphic mappings of a finite-dimensional space into a Banach space, Sibirsk. Mat. Zh. 31 (1990), no. 1, 161-171 (in Russian); English transl.: Siberian Math. J. 31 (1990), 137-146. 
  3. [3] S. Yu. Favorov, Estimates for asymptotic measures and Jessen functions for almost periodic functions, Dopov. Nats. Akad. Ukraïni 1996 (10), 27-30 (in Russian). Zbl0923.42007
  4. [4] Ye. A. Gorin and S. Yu. Favorov, Generalizations of Khinchin's inequality, Teor. Veroyatnost. i Primenen. 35 (1990), 763-767 (in Russian); English transl.: Theory Probab. Appl. 35 (1990), 766-771. Zbl0741.60013
  5. [5] Ye. A. Gorin and S. Yu. Favorov, Variants of the Khinchin inequality, in: Studies in the Theory of Functions of Several Real Variables, Yaroslavl', 1990, 52-63 (in Russian). 
  6. [6] J. P. Kahane, Some Random Series of Functions, Cambridge Univ. Press, New York, 1985. Zbl0571.60002
  7. [7] R. Latała, On the equivalence between geometric and arithmetic means for log-con-cave measures, in: Proceedings of Convex Geometry Seminar, MSRI, Berkeley, 1996, to appear. 
  8. [8] V.D. Milman and G. Schechtman, Asymptotic Theory of Finite Dimensional Normed Spaces, Lecture Notes in Math. 1200, Springer, 1986. Zbl0606.46013
  9. [9] D.C. Ullrich, Khinchine's inequality and the zeros of Bloch functions, Duke Math. J. 57 (1988), 519-535. Zbl0678.30006
  10. [10] D.C. Ullrich, An extension of the Kahane-Khinchine inequality in a Banach space, Israel J. Math. 62 (1988), 56-62. Zbl0654.46019

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