# A generalized Kahane-Khinchin inequality

Studia Mathematica (1998)

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

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topFavorov, 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

top- [1] S. Yu. Favorov, The distribution of values of holomorphic mappings of ${\u2102}^{n}$ 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] 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] 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] 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] 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] J. P. Kahane, Some Random Series of Functions, Cambridge Univ. Press, New York, 1985. Zbl0571.60002
- [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] V.D. Milman and G. Schechtman, Asymptotic Theory of Finite Dimensional Normed Spaces, Lecture Notes in Math. 1200, Springer, 1986. Zbl0606.46013
- [9] D.C. Ullrich, Khinchine's inequality and the zeros of Bloch functions, Duke Math. J. 57 (1988), 519-535. Zbl0678.30006
- [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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