The Riesz potential as a multilinear operator into general BMOβ spaces

Aimar, Hugo; Hartzstein, Silvia Inés; Iaffei, Bibiana; Viviani, Beatriz

doi:10.1007/s10958-011-0264-3

Cited by 7 publications

(9 citation statements)

References 10 publications

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“…We point out that other smoothing-type estimates have been proved for the bilinear fractional integral operators before. For example, in [1], Aimar et al proved that the I ν maps from products of Lebesgue spaces with appropriate indices into certain Campanato-BM O type spaces when 1 p 1 + 1 p 2 ≤ ν n . Such spaces provide the right setting when working on spaces of homogeneous type.…”

Section: Introductionmentioning

confidence: 99%

Smoothing properties of bilinear operators and Leibniz-type rules in Lebesgue and mixed Lebesgue spaces

Hart

Torres

2018

Trans. Amer. Math. Soc.

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We prove that bilinear fractional integral operators and similar multipliers are smoothing in the sense that they improve the regularity of functions. We also treat bilinear singular multiplier operators which preserve regularity and obtain several Leibniz-type rules in the contexts of Lebesgue and mixed Lebesgue spaces.Bényi-Torres [11] showed that for m = 0 these bilinear Calderón-Zygmund operators also satisfy for s > 0 and 1/p 1 + 1/p 2 = 1/q < 1 the estimate J s P a 0 (f, g)

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Section: Introductionmentioning

confidence: 99%

Smoothing properties of bilinear operators and Leibniz-type rules in Lebesgue and mixed Lebesgue spaces

Hart

Torres

2018

Trans. Amer. Math. Soc.

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“…The author also considered weighted versions of these estimates, generalizing the result in [5]. On the other hand, in [1] the authors proved unweighted estimates of I γ,m between m i=1 L p i and Lipschitz-δ spaces, with 0 ≤ δ < 1 and δ/n = γ/n − 1/p. For other type of estimates involving I γ,m see also [8].…”

Section: Introductionmentioning

confidence: 92%

“…In this paper we study the boundedness of the operator I γ,m between a product of weighted Lebesgue spaces and certain weighted Lipschitz spaces, generalizing the linear case proved in [7] and the unweighted problem given in [1]. We do not only consider related weights, which is an adequate extension of the one-weight estimates in the linear case, but also with independent weights exhibiting a generalization of the two-weight problem for m = 1.…”

Section: Introductionmentioning

confidence: 99%

Optimal parameters related with continuity properties of the multilinear fractional integral operator between Lebesgue and Lipschitz spaces

Berra¹,

Pradolini²,

Ramos³

2022

Preprint

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We deal with the boundedness of the multilinear fractional integral operator Iγ,m from a product of weighted Lebesgue spaces into adequate weighted Lipschitz spaces. Our results generalize some previous estimates not only for the linear case but also for the unweighted problem in the multilinear context. We characterize the classes of weights for which the problem described above holds and show the optimal range of the parameters involved. The optimality is understood in the sense that the parameters defining the corresponding spaces belong to a certain region. We further exhibit examples of weights for the class which cover the mentioned area.

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“…The author also considered weighted versions of these estimates, generalizing the results of [9] to the multilinear context. On the other hand, in [1] unweighted estimates of I γ,m between m i=1 L p i and Lipschitz-δ spaces were given, with 0 ≤ δ < 1 and δ = γ − n/p. For other type of estimates involving multilinear version of the fractional integral operator see also [3], [4], [6] and [13].…”

Section: Introductionmentioning

confidence: 99%

Two-weighted estimates of the multilinear fractional integral operator between weighted Lebesgue and Lipschitz spaces with optimal parameters

Berra¹,

Pradolini²,

Ramos³

2022

Preprint

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Given an m-tuple of weights v = (v1, . . . , vm), we characterize the classes of pairs (w, v) involved with the boundedness properties of the multilinear fractional integral operator from m i=1 L p i (v p i i ) into suitable Lipschitz spaces associated to a parameter δ, Lw(δ). Our results generalize some previous estimates not only for the linear case but also for the unweighted problem in the multilinear context. We emphasize the study related to the range of the parameters involved with the problem described above, which is optimal in the sense that they become trivial outside of the region obtained. We also exhibit nontrivial examples of pairs of weights in this region.This article is dedicated to Professor Eleonor "Pola" Harboure, beloved colleague whose vast knowledge and human kindness have always been a guidance to us.

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The Riesz potential as a multilinear operator into general BMOβ spaces

Cited by 7 publications

References 10 publications

Smoothing properties of bilinear operators and Leibniz-type rules in Lebesgue and mixed Lebesgue spaces

Smoothing properties of bilinear operators and Leibniz-type rules in Lebesgue and mixed Lebesgue spaces

Optimal parameters related with continuity properties of the multilinear fractional integral operator between Lebesgue and Lipschitz spaces

Two-weighted estimates of the multilinear fractional integral operator between weighted Lebesgue and Lipschitz spaces with optimal parameters

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