On a discrete bilinear singular operator

Dong Dong

doi:10.1016/j.crma.2017.03.010

On a discrete bilinear singular operator

Dong Dong

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We prove that for a large class of functions P and Q, the discrete bilinear operator T_P,Q(f,g)(n)=∑_m∈Z∖{0}f(n−P(m))g(n−Q(m))[Formula presented] is bounded from l²×l² into l^1+ϵ,∞ for any ϵ∈(0,1].

Original language	English (US)
Pages (from-to)	538-542
Number of pages	5
Journal	Comptes Rendus Mathematique
Volume	355
Issue number	5
DOIs	https://doi.org/10.1016/j.crma.2017.03.010
State	Published - May 2017

ASJC Scopus subject areas

General Mathematics

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title = "On a discrete bilinear singular operator",

abstract = "We prove that for a large class of functions P and Q, the discrete bilinear operator TP,Q(f,g)(n)=∑m∈Z∖{0}f(n−P(m))g(n−Q(m))[Formula presented] is bounded from l2×l2 into l1+ϵ,∞ for any ϵ∈(0,1].",

author = "Dong Dong",

note = "Publisher Copyright: {\textcopyright} 2017 Acad{\'e}mie des sciences",

year = "2017",

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doi = "10.1016/j.crma.2017.03.010",

language = "English (US)",

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N2 - We prove that for a large class of functions P and Q, the discrete bilinear operator TP,Q(f,g)(n)=∑m∈Z∖{0}f(n−P(m))g(n−Q(m))[Formula presented] is bounded from l2×l2 into l1+ϵ,∞ for any ϵ∈(0,1].

AB - We prove that for a large class of functions P and Q, the discrete bilinear operator TP,Q(f,g)(n)=∑m∈Z∖{0}f(n−P(m))g(n−Q(m))[Formula presented] is bounded from l2×l2 into l1+ϵ,∞ for any ϵ∈(0,1].

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DO - 10.1016/j.crma.2017.03.010

M3 - Article

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JF - Comptes Rendus Mathematique

IS - 5

ER -

On a discrete bilinear singular operator

Abstract

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