Tame L p -multipliers

Kathryn Hare

Colloquium Mathematicae (1993)

  • Volume: 64, Issue: 2, page 303-314
  • ISSN: 0010-1354

Abstract

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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 ( γ m ) = a m ( 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.

How to cite

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Hare, Kathryn. "Tame $L^p$-multipliers." Colloquium Mathematicae 64.2 (1993): 303-314. <http://eudml.org/doc/210194>.

@article{Hare1993,
abstract = {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.},
author = {Hare, Kathryn},
journal = {Colloquium Mathematicae},
keywords = {multipliers; tame measures; Fourier transform; Rajchman sets; Hardy space; complex Lie group},
language = {eng},
number = {2},
pages = {303-314},
title = {Tame $L^p$-multipliers},
url = {http://eudml.org/doc/210194},
volume = {64},
year = {1993},
}

TY - JOUR
AU - Hare, Kathryn
TI - Tame $L^p$-multipliers
JO - Colloquium Mathematicae
PY - 1993
VL - 64
IS - 2
SP - 303
EP - 314
AB - 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.
LA - eng
KW - multipliers; tame measures; Fourier transform; Rajchman sets; Hardy space; complex Lie group
UR - http://eudml.org/doc/210194
ER -

References

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