The multilinear Marcinkiewicz interpolation theorem revisited: The behavior of the constant

Grafakos, Loukas; Liu, Liguang; Lu, Shanzhen; Zhao, Fayou

doi:10.1016/j.jfa.2011.12.009

Cited by 29 publications

(25 citation statements)

References 10 publications

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“…The two main linear interpolation theorems, the Marcinkiewicz and Riesz-Thorin theorems, have well-established multilinear analogs. The works [9], [5], [2], [3] provide multilinear extensions of the Marcinkiewicz interpolation theorem. The Riesz-Thorin theorem is easily adapted in the multilinear case in [11,21,Chapter XII,(3.3)] and [1,Theorem 4.4.2]; related versions of this result have appeared in [10], [7], [8].…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

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Off-diagonal multilinear interpolation between adjoint operators

Grafakos

Lynch

2015

commath

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Section: Introduction and The Main Resultsmentioning

confidence: 99%

“…, 1 t , 1 s ). Then by the multilinear Marcinkiewicz interpolation theorem (see for instance [3]), it follows that T satisfies strong type bounds in H.…”

Section: The Proofmentioning

confidence: 99%

Off-diagonal multilinear interpolation between adjoint operators

Grafakos

Lynch

2015

commath

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“…When all p j > 1, the fact P (k) m+1 : L p0 × L p1 × · · · × L pm → L p is a consequence of the corresponding weak type estimate via multilinear interpolation, see [10]. It will therefore suffice to prove that P…”

Section: The Proof Of the Theorem 11mentioning

confidence: 98%

Multilinear paraproducts revisited

Grafakos¹,

He²,

Kalton³

et al. 2015

Rev. Mat. Iberoam.

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We prove that multilinear paraproducts are bounded from products of Lebesgue spaces L p 1 ×· · ·×L p m+1 to L p,∞ , when 1 ≤ p1, . . . , pm, pm+1 < ∞, 1/p1 + · · · + 1/pm+1 = 1/p. We focus on the endpoint case when some indices pj are equal to 1, in particular we obtain a new proof of the estimate L 1 × · · · × L 1 → L 1/(m+1),∞ .Mathematics Subject Classification (2010): Primary 42B20; Secondary 42E30.

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“…We can obtain the intermediate boundedness of S α by using of the bilinear interpolation via complex method adapted to the setting of analytic families or real method in [3]. Bernicot et al [1] described how to make use of real method.…”

Section: Appendix: Bilinear Interpolationmentioning

confidence: 99%

Bilinear Riesz means on the Heisenberg group

Wang

2019

Sci. China Math.

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In this article, we investigate the bilinear Riesz means S α associated to the sublaplacian on the Heisenberg group. We prove that the operator S α is bounded from L p 1 × L p 2 into L p for 1 ≤ p1, p2 ≤ ∞ and 1/p = 1/p1 + 1/p2 when α is large than a suitable smoothness index α(p1, p2). There are some essential differences between the Euclidean space and the Heisenberg group for studying the bilinear Riesz means problem. We make use of some special techniques to obtain a lower index α(p1, p2). Date

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The multilinear Marcinkiewicz interpolation theorem revisited: The behavior of the constant

Cited by 29 publications

References 10 publications

Off-diagonal multilinear interpolation between adjoint operators

Off-diagonal multilinear interpolation between adjoint operators

Multilinear paraproducts revisited

Bilinear Riesz means on the Heisenberg group

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