A pointwise estimate for positive dyadic shifts and some applications

By José M. Conde-Alonso, G. Rey. 2014

159 citations recorded by the source corpus.

We prove a (sharp) pointwise estimate for positive dyadic shifts of complexity m which is linear in the complexity. This can be used to give a pointwise estimate for Calderón-Zygmund operators and to answer a question originally posed by Lerner. Several applications to weighted estimates for both multilinear Calderón-Zygmund operators and square functions are discussed.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/523cece8393be79431336c1be5783cf3b134bf7e

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In Applied Mathematics

Citations in the corpus

Uniform sparse domination of singular integrals via dyadic shifts (2016, methodology): “The pointwise control of a Calderón-Zygmund operator T by 2d sparse averaging operators depending on T itself and on the input function f , (1.4) |T f (x)| ≤ C ∑ 1≤ j≤2d ∑ Q∈S j 〈 f 〉Q1Q(x) has been first achieved independently by Conde-Alonso and Rey [6] and Lerner and Nazarov [17], elaborating on ”
Intuitive dyadic calculus: The basics (2015, background): “, fmχQ[2] ](x)| > α}, we have |Gα| 6 ( C α m ∏”
A sparse domination principle for rough singular integrals (2016, unknown): “Introduction and main results Singular integral operators of Calderón-Zygmund type, which are a priori signed and nonlocal, can be dominated in norm [23], pointwise [8, 19, 22], or dually [2, 10, 11] by sparse averaging operators (forms), which are in contrast positive and localized.”
On pointwise estimates involving sparse operators (2015, background): “Rey [2], and by the author and F.”
On pointwise and weighted estimates for commutators of Calder\'on-Zygmund operators (2016, background): “In particular, it was recently discovered by several authors, first in [5,25] and subsequently refined in [19,21,24], (see also [1,8] for some interesting developments) that a Calderón–Zygmund operator is dominated pointwise by a finite number of sparse operators AS defined by ASf(x) = ∑ Q∈S fQχQ(x)”
Extrapolation for multilinear Muckenhoupt classes and applications (2018, background): “We start with an estimate proved independently and simultaneously in [10] and [26]: for any f, g ∈ C c (R ), one has”
Sparse Domination Theorem for Multilinear Singular Integral Operators with $L^{r}$-Hörmander Condition (2016, methodology): “3 [6] J. Conde-Alonso and G. Rey, A pointwise estimate for positive dyadic shifts and some applications, Math.”
Sparse bilinear forms for Bochner Riesz multipliers and applications (2016, unknown): “After that, Lerner-Nazarov [26] and Conde-Rey [11] simultaneously simplified the norm control by a pointwise bound.”