Weighted compact commutator of bilinear Fourier multiplier operator

Hu, Guoen

doi:10.1007/s11401-017-1096-3

Cited by 6 publications

(4 citation statements)

References 18 publications

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“…Accordingly, together with (5.14) applied to m ∈ W s (R nm ) and (5.16), Corollary 1.4 with p Corollary 4]. On the other hand, by enlarging the range of p to the case p ≤ 1, Theorems 5.6 and 5.7 respectively refines the compactness on weighted Lebesgue spaces in [38] and [62,Theorem 2].…”

Section: Multilinear Fourier Multipliers Formentioning

confidence: 99%

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Extrapolation for multilinear compact operators and applications

Cao¹,

Olivo²,

Yabuta³

2020

Preprint

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This paper is devoted to studying the Rubio de Francia extrapolation for multilinear compact operators. It allows one to extrapolate the compactness of T from just one space to the full range of weighted spaces, whenever an m-linear operator T is bounded on weighted Lebesgue spaces. This result is indeed established in terms of the multilinear Muckenhoupt weights A p, r , and the limited range of the L p scale. To show extrapolation theorems above, by means of a new weighted Fréchet-Kolmogorov theorem, we present the weighted interpolation for multilinear compact operators. As applications, we obtain the weighted compactness of commutators of many multilinear operators, including multilinear ω-Calderón-Zygmund operators, multilinear Fourier multipliers, bilinear rough singular integrals and bilinear Bochner-Riesz means. Beyond that, we establish the weighted compactness of higher order Calderón commutators, and commutators of Riesz transforms related to Schrödinger operators.

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Section: Multilinear Fourier Multipliers Formentioning

confidence: 99%

“…Let us present a result about the compactness of T m . Indeed, modifying the proof of [38,Theorem 1.1] to the m-linear case, we get that for every b ∈ CMO and for each j = 1, . .…”

Section: Multilinear Fourier Multipliers Formentioning

confidence: 99%

Extrapolation for multilinear compact operators and applications

Cao¹,

Olivo²,

Yabuta³

2020

Preprint

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“…In addition, Hu [17] introduced another kind of bilinear maximal operators M 1 β and M 2 β which was defined by…”

Section: A Multilinear Maximal Operatormentioning

confidence: 99%

“…It is easy to find that the condition (a) holds because of the boundedness of [b, T δ ] 1 in Theorem 2. Now, we prove the condition (b) using some ideas in [17]. Let R > 0 be large enough such that supp b ⊂ B(0, R) and let A ≥ max(2R, 1), l be a nonnegative integer.…”

Section: Proof Of Theoremmentioning

confidence: 99%

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

Chen

2019

Appl. Math. J. Chin. Univ.

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In this paper, the behavior for commutators of a class of bilinear singular integral operator associated with non-smooth kernels on the products of weighted Lebesgue spaces is considered. By some new maximal functions to control the commutators of bilinear singular integral operators and CMO functions, compactness of the commutators is proved.2000 Mathematics Subject Classification. Primary 42B20, 47B07; Secondary 42B25.

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