Idempotents of Fourier multiplier algebra

Лебедев, В. В.; Olevskii, Alexander

doi:10.1007/bf01896407

Cited by 23 publications

(27 citation statements)

References 6 publications

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“…Part (i), as mentioned earlier, is due to V. Lebedev and A. Olevskiõ Ï [4]. Part (ii) can be deduced from (i).…”

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confidence: 70%

“…For the particular group R n it has been shown by V. Lebedev and A. Olevskiõ Ï [4] that for a measurable subset E & R n to generate an idempotent p-multiplier c E one has to put stringent restrictions on the topology of the set E, namely E must coincide almost everywhere with an open set. The aim of this note is to clarify the dependence on p of idempotent p-multipliers for the group R n .…”

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confidence: 99%

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Idempotent multipliers for LP $(\Bbb R)$

Mockenhaupt¹,

Ricker²

2000

Arch. Math.

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The algebra b p R, p P 1Y I n f2g, consisting of all measurable sets in R whose characteristic function is a Fourier p-multiplier, forms an algebra of sets containing many interesting and non-trivial elements (e.g. all intervals and their finite unions, certain periodic sets, arbitrary countable unions of dyadic intervals, etc.). However, b p R fails to be a s-algebra. It has been shown by V. Lebedev and A. Olevskiõ Ï [4] that if E P b p R, then E must coincide a.e. with an open set, a remarkable topological constraint on E. In this note we show if 2`p`I , then there exists E P b p R which is not in b q R for any q b p.

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“…Part (i), as mentioned earlier, is due to V. Lebedev and A. Olevskiõ Ï [4]. Part (ii) can be deduced from (i).…”

mentioning

confidence: 70%

mentioning

confidence: 99%

Idempotent multipliers for LP $(\Bbb R)$

Mockenhaupt¹,

Ricker²

2000

Arch. Math.

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show abstract

“…The motivation for this paper comes from the beautiful work of V. Lebedev and A. Olevskiȋ [6] on the classical Fouirer multipliers. We will prove an analogue of their result in the context of bi-linear multiplier operators.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%