The Sharp Weighted Bound for Multilinear Maximal Functions and Calderón–Zygmund Operators

Li, Kangwei; Moen, Kabe; Sun, Wenchang

doi:10.1007/s00041-014-9326-5

Cited by 51 publications

(45 citation statements)

References 17 publications

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“…In the linear setting this result is based on Buckley's sharp weighted bound for the Hardy-Littlewood maximal operator. This bound has been generalized to the multi-sublinear Hardy-Littlewood maximal operator by Damián, Lerner, and Pérez [DLP15] to a sharp estimate in the setting of a mixed type A p -A ∞ estimates and a sharp A p bound is found in [LMS14]. We give a different proof of this result for the limited range version of this maximal operator by generalizing a proof of Lerner [Ler08].…”

Section: Introductionmentioning

confidence: 83%

Quantitative estimates and extrapolation for multilinear weight classes

Nieraeth

2019

Math. Ann.

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In this paper we prove a quantitative multilinear limited range extrapolation theorem which allows us to extrapolate from weighted estimates that include the cases where some of the exponents are infinite. This extends the recent extrapolation result of Li, Martell, and Ombrosi. We also obtain vector-valued estimates including ℓ ∞ spaces and, in particular, we are able to reprove all the vector-valued bounds for the bilinear Hilbert transform obtained through the helicoidal method of Benea and Muscalu. Moreover, our result is quantitative and, in particular, allows us to extend quantitative estimates obtained from sparse domination in the Banach space setting to the quasi-Banach space setting.Our proof does not rely on any off-diagonal extrapolation results and we develop a multilinear version of the Rubio de Francia algorithm adapted to the multisublinear Hardy-Littlewood maximal operator.As a corollary, we obtain multilinear extrapolation results for some upper and lower endpoints estimates in weak-type and BMO spaces.2010 Mathematics Subject Classification. 42B20, 42B25.

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Section: Introductionmentioning

confidence: 83%

Quantitative estimates and extrapolation for multilinear weight classes

Nieraeth

2019

Math. Ann.

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“…To prove this theorem, we borrow some ideas in [28,Theorem 3.2]. However, we refine the argument in [28, Theorem 3.2] to provide a direct proof, and hence we avoid a duality argument for multilinear operators which may not be applicable in our setting.…”

Section: Proof Of Main Resultsmentioning

confidence: 99%

“…The versatility of Lerner's techniques is reflected in the extension of (1.3) and the A 2 theorem to multilinear Calderón-Zygmund operators in [10]. Later on, Li, Moen and Sun in [28] proved the corresponding sharp weighted A P bounds for multilinear sparse operators. In other words, if 1 < p 1 , .…”

Section: Introductionmentioning

confidence: 99%

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Weighted Bounds for Multilinear Square Functions

Bui¹,

Hormozi

2016

Potential Anal

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Abstract. Let P = (p1, . . . , pm) with 1 < p1, . . . , pm < ∞, 1/p1 + · · · + 1/pm = 1/p and w = (w1, . . . , wm) ∈ A P . In this paper, we investigate the weighted bounds with dependence on aperture α for multilinear square functions S α,ψ ( f ). We show thatThis result extends the result in the linear case which was obtained by Lerner in 2014. Our proof is based on the local mean oscillation technique presented firstly to find the weighted bounds for Calderón-Zygmund operators. This method helps us avoiding intrinsic square functions in the proof of our main result.

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“…Recently, Li, Moen and Sun [18] obtained the following A p type estimate which improved the result in [16].…”

Section: Furthermore This Estimate Is Sharpmentioning

confidence: 89%