A generalized Kahane-Khinchin inequality
Volume 130 / 1998
Studia Mathematica 130 (1998), 101-107
DOI: 10.4064/sm-130-2-101-107
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 $e^{2πiφ}$.
