2019
DOI: 10.1007/s12220-019-00297-x
|View full text |Cite
|
Sign up to set email alerts
|

Quantitative Weighted Estimates for Rubio de Francia’s Littlewood–Paley Square Function

Abstract: We consider the Rubio de Francia's Littlewood-Paley square function associated with an arbitrary family of intervals in R with finite overlapping. Quantitative weighted estimates are obtained for this operator. The linear dependence on the characteristic of the weight [w] A p/2 turns out to be sharp for 3 ≤ p < ∞, whereas the sharpness in the range 2 < p < 3 remains as an open question. The results arise as a consequence of a sparse domination shown for these operators, obtained by suitably adapting the ideas … Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1

Citation Types

0
3
0

Year Published

2020
2020
2022
2022

Publication Types

Select...
4
1

Relationship

0
5

Authors

Journals

citations
Cited by 5 publications
(3 citation statements)
references
References 39 publications
0
3
0
Order By: Relevance
“…For more details on Littlewood-Paley square functions of Rubio de Francia type, see [29] and the references therein. For sparse bounds for Littlewood-Paley operators of Rubio de type and for Marcinkiewicz-type multiplier operators in the Walsh-Fourier setting, see [15,22], respectively.…”
Section: Introductionmentioning
confidence: 99%
“…For more details on Littlewood-Paley square functions of Rubio de Francia type, see [29] and the references therein. For sparse bounds for Littlewood-Paley operators of Rubio de type and for Marcinkiewicz-type multiplier operators in the Walsh-Fourier setting, see [15,22], respectively.…”
Section: Introductionmentioning
confidence: 99%
“…Using [74,Lemma 4.5] one can check the weak L 2 -boundedness of our sharp grand maximal truncation operator, which by Theorem 1.1 and Proposition 4.1 yields sparse domination and weighted estimates for vector-valued Littlewood-Paley-Rubio de Francia estimates. In the scalar case, sparse domination was shown by Garg, Roncal, and Shrivastava [29] using time-frequency analysis. • Theorem 3.4 can be used to show sparse domination and sharp weighted estimates for fractional integral operators as in [16][17][18]47].…”
Section: Further Applicationsmentioning
confidence: 96%
“…The A 2 -theorem had been established by Hytönen in [38]. Sparse arguments have bee used to study quantitative L p -weighted inequalities for several class of operators (see [1], [10], [23], [31], [43], [49], [50], [51], [52], [53], [54], [56], [61] and the reference therein).…”
Section: Introductionmentioning
confidence: 99%