On the optimal numerical parameters related with two weighted estimates for commutators of classical operators and extrapolation results

Pradolini, Gladis; Ramos, Wilfredo; Recchi, Jorgelina

doi:10.1007/s13348-020-00287-1

Cited by 6 publications

(11 citation statements)

References 41 publications

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“…and, in this sense, this is an optimal estimate. Similar results in this spirit were proved in [12] for commutators of singular integral and fractional type operators, by considering the Lipschitz spaces given in [11].…”

Section: Introductionsupporting

confidence: 72%

“…In this paper we prove two-weighted norm estimates for singular integral and fractional type operators and their higher order commutators between weighted L p and certain spaces related to a parameter β, that include Lipschitz, BMO and Morrey spaces and that are wider than those considered in [12]. Moreover the classes of weights are quite different from those given there, including local and global conditions.…”

Section: Introductionmentioning

confidence: 91%

“…In [12] the authors prove two weighted boundedness results for commutators of a great variety of operators between Lebesgue and Lipschitz spaces L w (β). These spaces collect the functions…”

Section: Operators With Lipschitz Regularitymentioning

confidence: 99%

“…then the classes H(r, α, δ) defined in [12] are contained in the classes H(r, α, δ). We shall prove later that this inclusion is strict.…”

Section: Operators With Lipschitz Regularitymentioning

confidence: 99%

“…We prove that a one-weight result can only holds whenever the relation between the parameters is standard. We also give the relation between our classes of weights and those given in [12], which are natural extensions of the A 1 -Muckenhoupt class in the one-weight estimates.…”

Section: Introductionmentioning

confidence: 98%

See 4 more Smart Citations

On optimal parameters involved with two-weighted estimates of commutators of singular and fractional integral operators

Pradolini¹,

Recchi²

2019

Preprint

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In this paper we prove two-weighted norm estimates for higher order commutator of singular integral and fractional type operators between weighted L p and certain spaces that include Lipschitz, BMO and Morrey spaces. We also give the optimal parameters involved with these results, where the optimality is understood in the sense that the parameters defining the corresponding spaces belong to certain region out of which the classes of weights are satisfied by trivial weights. We also exhibit pairs of non-trivial weights in the optimal region satisfying the conditions required.

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Section: Introductionsupporting

confidence: 72%

Section: Introductionmentioning

confidence: 91%

Section: Operators With Lipschitz Regularitymentioning

confidence: 99%

“…then the classes H(r, α, δ) defined in [12] are contained in the classes H(r, α, δ). We shall prove later that this inclusion is strict.…”

Section: Operators With Lipschitz Regularitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

See 3 more Smart Citations

On optimal parameters involved with two-weighted estimates of commutators of singular and fractional integral operators

Pradolini¹,

Recchi²

2019

Preprint

Self Cite

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

2023

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We prove continuity properties of higher order commutators of fractional operators on the multilinear setting, between a product of weighted Lebesgue spaces into certain weighted Lipschitz spaces. The considered operators include the multilinear fractional integral function and the main results extend previous estimates known for the unweighted case, as well as those established on the linear case.We give a complete study showing the main properties of the related multilinear weights and the optimal region described by the parameters where we can find nontrivial examples, including the restricted case of the one-weight theory. We also exhibit examples of such weights on the whole region.

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On optimal parameters involved with two-weighted estimates of commutators of singular and fractional operators with Lipschitz symbols

Pradolini¹,

Recchi²

2023

Czech.Math.J.

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On the optimal numerical parameters related with two weighted estimates for commutators of classical operators and extrapolation results

Cited by 6 publications

References 41 publications

On optimal parameters involved with two-weighted estimates of commutators of singular and fractional integral operators

On optimal parameters involved with two-weighted estimates of commutators of singular and fractional integral operators

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

On optimal parameters involved with two-weighted estimates of commutators of singular and fractional operators with Lipschitz symbols

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