The Herz–Schur multiplier norm of sets satisfying the Leinert condition
Volume 124 / 2011
Colloquium Mathematicum 124 (2011), 255-274
MSC: Primary 43A22, 46L07, 47L07.
DOI: 10.4064/cm124-2-10
Abstract
It is well known that in a free group $\def\F{{\mathbb F}}\F$, one has $\def\F{{\mathbb F}}\|\chi_E\|_{M_{cb}A(\F)}\leq 2$, where $E$ is the set of all the generators. We show that the (completely) bounded multiplier norm of any set satisfying the Leinert condition depends only on its cardinality. Consequently, based on a result of Wysoczański, we obtain a formula for $\def\F{{\mathbb F}}\|\chi_E\|_{M_{cb}A(\F)}$.
