Endpoint estimates for commutators of multilinear fractional integral operators

Yu, Xiao; Chen, Jie Cheng

doi:10.1007/s10114-010-8421-z

Cited by 8 publications

(3 citation statements)

References 17 publications

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“…Subsequently, in the celebrated work [27] Lerner et al removed the restriction of that p > 1 and established the multiple weighted version as well as the weak-type endpoint estimate, and see [1,7] for the non-smooth kernels cases. The corresponding results for the commutators of multilinear fractional integrals were given by Chen and Xue [11] (see also [45,8]). Recently, Chaffee [4] obtained the following characterized theorem.…”

Section: Examples and Applicationsmentioning

confidence: 86%

The Unified Theory for the Necessity of Bounded Commutators and Applications

Guo

Lian

2019

J Geom Anal

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The general methods which are powerful for the necessity of bounded commutators are given. As applications, some necessary conditions for bounded commutators are first obtained in certain endpoint cases, and several new characterizations of BM O spaces, Lipschitz spaces and their weighted versions via boundedness of commutators in various function spaces are deduced.2010 Mathematics Subject Classification. 42B20; 42B25.

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Section: Examples and Applicationsmentioning

confidence: 86%

The Unified Theory for the Necessity of Bounded Commutators and Applications

Guo

Lian

2019

J Geom Anal

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“…This is motivated by the results due to Lacey and Thiele [6][7][8]. Recently many people are studying these operators from a various points of view [9][10][11][12][13][14].…”

Section: Remark 17mentioning

confidence: 99%

Multilinear fractional integrals on Morrey spaces

Iida

Sato

Sawano

et al. 2012

Acta. Math. Sin.-English Ser.

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“…The multilinear fractional integral operators were also investigated by Kenig and Stein [9]. Recently many people have been studying these operators from various points of view [8,13,15,18].…”

Section: Introductionmentioning

confidence: 99%

Generalized higher commutators generated by the multilinear fractional integrals and Lipschitz functions

Yu²,

Zhou³

2014

Turk J Math

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Let l ∈ N and ⃗ A = (A1, . . . , A l ) and ⃗ f = (f1, . . . , f l ) be 2 finite collections of functions, where every function Ai has derivatives of order mi and f1, . .Suppfi. The generalized higher commutator generated by the multilinear fractional integral is then given bythe authors establish the boundedness of I ⃗ A α,m on the product Lebesgue space, Triebel-Lizorkin space, and Lipschitz space.

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Endpoint estimates for commutators of multilinear fractional integral operators

Cited by 8 publications

References 17 publications

The Unified Theory for the Necessity of Bounded Commutators and Applications

The Unified Theory for the Necessity of Bounded Commutators and Applications

Multilinear fractional integrals on Morrey spaces

Generalized higher commutators generated by the multilinear fractional integrals and Lipschitz functions

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