Intuitive dyadic calculus: The basics

By Andrei K. Lerner, Fedor Nazarov. Expositiones mathematicae, 2015

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This book is a short introduction into dyadic analysis with applications to classical weighted norm inequalities.

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Weighted Norm Inequalities for Rough Singular Integral Operators (2017, background): “For a more detailed account about dyadic lattices and sparse families we remit to [33].”
Quantitative estimates and extrapolation for multilinear weight classes (2018, methodology): “See [29] for further properties and results regarding sparse collections of cubes.”
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): “1, 2, 3, 5 [21] A. Lerner and F. Nazarov, Intuitive dyadic calculus: the basics.”