Compactness for the commutators of multilinear singular integral operators with non-smooth kernels

Bu, Rui; Chen, Jiecheng

doi:10.1007/s11766-019-3501-z

Cited by 11 publications

(6 citation statements)

References 32 publications

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“…In [5,30,36], the following weighted boundedness results about the bilinear Calderón-Zygmund operator associated with kernel K and its commutators were obtained: 6.4. Theorem ([5], Theorem 1.2, [30], Corollary 3.9, Theorem 3.18 and [36], Theorem 1.1).…”

Section: Commutators Of Bilinear Calderón-zygmund Operatorsmentioning

confidence: 99%

“…Remark. The boundedness of T in [5] is not explicitly stated as a theorem but it is implicitly contained in the proof of the boundedness of the commutator. As explained in [5, Theorem 1.2], [30, Corollary 3.9 and Theorem 3.18] and [36, Theorem 1.1] all the previous bounds for iterated commutators hold for 0 < p < ∞.…”

Section: 7mentioning

confidence: 99%

“…The compactness of the commutator [T, b] α was considered by Bényi-Torres [1] and Bu-Chen [5] in the unweighted case: 1) and (2) of Theorem 6.4.…”

Section: 7mentioning

confidence: 99%

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Extrapolation of compactness on weighted spaces: Bilinear operators

Hytönen,

Lappas

2020

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In two previous papers, we obtained several "compact versions" of Rubio de Francia's weighted extrapolation theorem, which allowed us to extrapolate the compactness of linear operators from just one space to the full range of weighted Lebesgue spaces, where these operators are bounded. In this paper, we study the extrapolation of compactness for bilinear operators in terms of bilinear Muckenhoupt weights. As applications, we easily recover and improve earlier results on the weighted compactness of commutators of bilinear Calderón-Zygmund operators, bilinear fractional integrals and bilinear Fourier multipliers. More general versions of these results are recently due to Cao, Olivo and Yabuta (arXiv:2011.13191), whose approach depends on developing weighted versions of the Fréchet-Kolmogorov criterion of compactness, whereas we avoid this by relying on "softer" tools, which might have an independent interest in view of further extensions of the method.

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Section: Commutators Of Bilinear Calderón-zygmund Operatorsmentioning

confidence: 99%

Section: 7mentioning

confidence: 99%

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Extrapolation of compactness on weighted spaces: Bilinear operators

Hytönen,

Lappas

2020

Preprint

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“…Since then, this subject has attracted much attention. We refer the reader to [14,[24][25][26]31] for the compactness of commutators of multilinear operators. Very recently, extrapolation for linear and multilinear compact operators with applications were given by Cao et.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Bu and Chen [24] studied this question and they showed that the commutators of bilinear singular integral operators are compact from…”

Section: Introductionmentioning

confidence: 99%

On weighted Compactness of commutators of bilinear maximal Calderón-Zygmund singular integral operators

Wang,

Xue

2020

Preprint

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Let T be a bilinear Calderón-Zygmund singular integral operator and T * be its corresponding truncated maximal operator. For any b ∈ BMO(R n ) and bbe the commutators in the j-th entry and the iterated commutators of T * , respectively. In this paper, for all 1Since then, the study on the compactness of commutators of different operators has attracted much more attention. For examples, the compactness of commutators of the linear Fourier multipliers and pseudodifferential operators was considered by Cordes [13]. Beatrous and Li [1] studied the boundedness and compactness of the commutators of Hankel type operators. Krantz and Li [19],[20] applied the compactness characterization of the commutator [b, T Ω ] to study Hankel type operators on Bergman space. Wang [28] showed that the commutators of fractional integral operator are compact form L p (R n ) to L q (R n ). In 2009, Chen and Ding [8] proved thar the commutator of singular integrals with variable kernels is compact on L p (R n ) if and only if b ∈ CMO(R n ) and they also establised the compactness of Littlewood-Paley square functions in [9]. Later on, Chen, Ding and Wang [10] obtained the compactness of commutators for Marcinkiewicz Integral in Morrey Spaces. Recently, Liu, Wang and Xue [23] showed the compactness of the commutator of oscillatory singular integrals with non-convolutional type kernels.

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