Estimates for the commutator of bilinear Fourier multiplier

Hu, Guoen; Yi, Wentan

doi:10.1007/s10587-013-0074-5

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Cited by 4 publications

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“…By a suitable kernel estimate and the theory of multilinear singular integral operator, Bui and Duong [9] established the weighted estimates with multiple weights for when satisfies (3) for = 2 and ∈ ( , 2 ]. Hu and Yi [10] considered the behavior on 1 (R ) × ⋅ ⋅ ⋅ × (R ) for ,Σ when satisfies (5) for 1 , . .…”

Section: Introductionmentioning

confidence: 99%

Compactness of the Commutator of Multilinear Fourier Multiplier Operator on Weighted Lebesgue Space

Zhou

Peng

2014

Journal of Function Spaces

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LetTσbe the multilinear Fourier multiplier operator associated with multiplierσsatisfying the Sobolev regularity thatsupl∈ZσlWs1,…,sm(Rmn)<∞for somesk∈(n/2,n] (k=1,…,m). The authors prove that ifb1,…,bm∈BMO(Rn)andw⃗∈∏k=1m‍Apk/tk(tk=n/sk), then the commutatorTσ,Σbis bounded fromLp1(Rn,w1)×⋯×Lpm(Rn,wm)toLp(Rn,νw⃗). Moreover, the authors also prove that ifb1,…,bm∈VMO(Rn)andw⃗∈∏k=1m‍Apk/tk(tk=n/sk), then the commutatorTσ,Σbis compact operator fromLp1(Rn,w1)×⋯×Lpm(Rn,wm)toLp(Rn,νw⃗).

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Section: Introductionmentioning

confidence: 99%