On pointwise estimates involving sparse operators

By Andrei K. Lerner. 2015

192 citations recorded by the source corpus.

We obtain an alternative approach to recent results by M. Lacey \cite{La} and T. Hyt\"onen {\it et al.} \cite{HRT} about a pointwise domination of $\omega$-Calder\'on-Zygmund operators by sparse operators. This approach is rather elementary and it also works for a class of non-integral singular operators.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9df95fa2225baf7de5518e5701367538c7cf634f

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

On pointwise and weighted estimates for commutators of Calder\'on-Zygmund operators (2016, background): “An alternative proof of this result was obtained by the first author [24].”
Uniform sparse domination of singular integrals via dyadic shifts (2016, unknown): “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 ”
Sparse Domination Theorem for Multilinear Singular Integral Operators with $L^{r}$-Hörmander Condition (2016, background): “1, 2, 3, 5 [21] A. Lerner and F. Nazarov, Intuitive dyadic calculus: the basics.”
Two Weight Commutators on Spaces of Homogeneous Type and Applications (2018, methodology): “Here we can adapt the proof in [30] to our setting of spaces of homogeneous type.”
Some Remarks on the Pointwise Sparse Domination (2019, methodology): “This result is well known (see [19] and the history therein).”
Sparse bounds for maximal rough singular integrals via the Fourier transform (2017, background): “The dual pointwise version was first obtained in this form in [16] quantifying the initial result of Lacey [19]; see also [24].”