Boundedness of Commutators With Lipschitz Functions in Non-Homogeneous Spaces

Xiaoli,; Fu, Pengcheng; Yan, Victoria C.; Meng,; Dachun,

doi:10.11650/twjm/1500404567

Cited by 19 publications

(22 citation statements)

References 22 publications

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“…Remark 2.7. When m = 1, w = 1 and T α = I α the result above was proved in [25] in a more general context of non-homogeneous spaces. Certainly, their result was inspired in the article of [19], where the same result is proved for m = 1, w = 1, T α = I α and b ∈ BM O.…”

Section: Fractional Integral Operators With Lipschitz Regularitymentioning

confidence: 84%

The Effect of the Smoothness of Fractional Type Operators Over Their Commutators with Lipschitz Symbols on Weighted Spaces

Dalmasso

Pradolini

Ramos

2018

FCAA

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We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including L p -L q , L p -BM O and L p -Lipschitz estimates. The kernels of such operators satisfy certain size condition and a Lipschitz type regularity, and the symbol of the commutator belongs to a Lipschitz class. We also deal with commutators of fractional type operators with less regular kernels satisfying a Hörmander's type inequality. As far as we know, these last results are new even in the unweighted case. Moreover, we give a characterization result involving symbols of the commutators and continuity results for extreme values of p.

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Section: Fractional Integral Operators With Lipschitz Regularitymentioning

confidence: 84%

The Effect of the Smoothness of Fractional Type Operators Over Their Commutators with Lipschitz Symbols on Weighted Spaces

Dalmasso

Pradolini

Ramos

2018

FCAA

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“…The commutators of fractional type operators with Lipschitz symbols were studied by several authors. For instance, in [12] the authors considered unweighted estimates for the mentioned operator acting between different Lebesgue spaces in the context of non-doubling measures.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Commutators of potential type operators with Lipschitz symbols on variable Lebesgue spaces with different weights

Melchiori¹,

Pradolini²,

Ramos³

2019

Mathematical Inequalities &Amp; Applications

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We prove that a generalized Fefferman-Phong type condition on a pair of weights u and v is sufficient for the boundedness of the commutators of potential type operators from Lu . We also give an improvement of this result in the sense that we not only consider a variable version of power bump conditions, but also weaker norms related to Musielak-Orlicz functions.We consider a wider class of symbols including Lipschitz symbols and some generalizations.2010 Mathematics Subject Classification: 42B25

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“…• Theorems 5.6.5 and 5.6.8 were established by Hu et al in [54]. See Meng and Yang [97] for the boundedness of commutators generated by Calderón-Zygmund operators or fractional integrals with Lipschitz functions in the Lebesgue space and the Hardy space. • In [96], Meng and Yang obtained the boundedness in some Hardy-type spaces of multilinear commutators generated by Calderón-Zygmund operators or fractional integrals with RBMO .…”

Section: Notesmentioning

confidence: 98%