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The Herz-Schur multiplier norm of sets satisfying the Leinert condition

Éric Ricard; Ana-Maria Stan — 2011

Colloquium Mathematicae

It is well known that in a free group , one has $| | χ_{E} {| |}_{M_{c b} A ()} \leq 2$ , 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 $| | χ_{E} {| |}_{M_{c b} A ()}$ .

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