Tame $L^p$-multipliers
Tom 64 / 1993
Colloquium Mathematicum 64 (1993), 303-314
DOI: 10.4064/cm-64-2-303-314
Streszczenie
We call an $L^{p}$-multiplier m tame if for each complex homomorphism χ acting on the space of $L^{p}$ multipliers there is some $γ_{0} ∈ Γ$ and |a| ≤ 1 such that $χ(γm) = am(γ_{0}γ)$ for all γ ∈ Γ. Examples of tame multipliers include tame measures and one-sided Riesz products. Tame multipliers show an interesting similarity to measures. Indeed we show that the only tame idempotent multipliers are measures. We obtain quantitative estimates on the size of $L^{p}$-improving tame multipliers which are similar to those obtained for measures, but are false for non-tame multipliers. One-sided Riesz products are seen to play a similar role in the study of tame multipliers as Riesz products do in the study of measures.
