A $B_p$ condition for the strong maximal function

Liu, Liguang; Luque, Teresa

doi:10.1090/s0002-9947-2014-05956-4

Cited by 15 publications

(18 citation statements)

References 29 publications

(37 reference statements)

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“…The boundedness of those operators on L p spaces was thoroughly studied by C. Pérez [30], under the aditional condition that A is doubling, assumption that was proved to be superfluous by Liu and Luque [24]. The condition is the following…”

Section: 21mentioning

confidence: 99%

Sharp $$A_{1}$$ Weighted Estimates for Vector-Valued Operators

Isralowitz

Pott²,

Rivera-Rı́os³

2020

J Geom Anal

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Given 1 ≤ q < p < ∞, quantitative weighted L p estimates, in terms of Aq weights, for vector valued maximal functions, Calderón-Zygmund operators, commutators and maximal rough singular integrals are obtained. The results for singular operators will rely upon suitable convex body domination results, which in the case of commutators will be provided in this work, obtaining as a byproduct a new proof for the scalar case as well.

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Section: 21mentioning

confidence: 99%

Sharp $$A_{1}$$ Weighted Estimates for Vector-Valued Operators

Isralowitz

Pott²,

Rivera-Rı́os³

2020

J Geom Anal

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“…Later on L. Liu and T. Luque [27], proved that imposing the doubling condition on A is superfluous. Now we compile some examples of maximal operators related to certain Young functions.…”

Section: Young Functions and Orlicz Spacesmentioning

confidence: 99%

Sparse and weighted estimates for generalized Hörmander operators and commutators

Ibañez-Firnkorn

Rivera-Rı́os

2019

Monatsh Math

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In this paper a pointwise sparse domination for generalized Hörmander and also for iterated commutators with those operators is provided generalizing the sparse domination result in [24]. Relying upon that sparse domination a number of quantitative estimates are derived. Some of them are improvements and complementary results to those contained in a series of papers due to M. Lorente, J. M. Martell, C. Pérez, S. Riveros and A. de la Torre [30,29,28]. Also the quantitative endpoint estimates in [24] are extended to iterated commutators. Other results that are obtained in this work are some local exponential decay estimates for generalized Hörmander operators in the spirit of [34] and some negative results concerning Coifman-Fefferman estimates for a certain class of kernels satisfying particular generalized Hörmander conditions.2000 Mathematics Subject Classification. 42B20, 42B25.

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“…Their covering lemma is quite useful by the reason that it overcomes the failure of the Besicovitch covering argument for rectangles with arbitrary eccentricities. The selection algorithm given by Córboda and Fefferman was used many times to gain end-point estimates for M R , as demonstrated in [5], [8], [11], [13], [21], [22], [23], [25]. The corresponding weighted version of (1.1) with w ∈ A 1,R was shown by Bagby and Kurtz [1].…”

Section: Introductionmentioning

confidence: 99%

“…Subsequently, under more weaker condition (Tauberian condition) than v ∈ A ∞,B , Liu and Luque [21] investigated the strong boundedness of two-weighted inequality for the maximal operator M B . They showed that if M B satisfies the Tauberian condition (condition (A) [12], [16], [29]) with respect to some γ ∈ (0, 1) and a weight µ as follows: there exists a positive constant C B,γ,µ such that, for all measurable sets E, it holds that…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the works in [2], [11] and [21], in this paper, we will investigate the boundedness of multilinear strong and fractional strong maximal operators in the setting of rectangles and in the setting of more general basis. We are mainly concerned with the end-point behavior, characterizations of two weighted norm inequalities and vector-valued norm inequalities.…”

Section: Introductionmentioning

confidence: 99%

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On the boundedness of multilinear fractional strong maximal operators with multiple weights

2019

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In this paper, we investigated the boundedness of multilinear fractional strong maximal operator MR,α associated with rectangles or related to more general basis with multiple weights A ( p,q),R . In the rectangles setting, we first gave an end-point estimate of MR,α, which not only extended the famous linear result of Jessen, Marcinkiewicz and Zygmund, but also extended the multilinear result of Grafakos, Liu, Pérez and Torres (α = 0) to the case 0 < α < mn. Then, in one weight case, we gave several equivalent characterizations between MR,α and A ( p,q),R , by applying a different approach from what we have used before. Moreover, a sufficient condition for the two weighted norm inequality of MR,α was presented and a version of vector-valued two weighted inequality for the strong maximal operator was established when m = 1. In the general basis setting, we further studied the properties of the multiple weights A ( p,q),R conditions, including the equivalent characterizations and monotonic properties, which essentially extended one's previous understanding. Finally, a survey on multiple strong Muckenhoupt weights was given, which demonstrates the properties of multiple weights related to rectangles systematically.Date: December 28, 2015.

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A $B_p$ condition for the strong maximal function

Cited by 15 publications

References 29 publications

Sharp $$A_{1}$$ Weighted Estimates for Vector-Valued Operators

Sharp $$A_{1}$$ Weighted Estimates for Vector-Valued Operators

Sparse and weighted estimates for generalized Hörmander operators and commutators

On the boundedness of multilinear fractional strong maximal operators with multiple weights

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