Intuitive dyadic calculus: The basics

Andrei K. Lerner; Fedor Nazarov

doi:10.1016/j.exmath.2018.01.001

Intuitive dyadic calculus: The basics

Andrei K. Lerner, Fedor Nazarov

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

92 Scopus citations

Abstract

This article is divided into two parts. In the first part we present a general theory of the dyadic lattices. In the second part we show several applications of this theory to harmonic analysis: a decomposition of an arbitrary measurable function in terms of its local mean oscillations, and a pointwise bound of Calderón–Zygmund operators by sparse operators.

Original language	English
Pages (from-to)	225-265
Number of pages	41
Journal	Expositiones Mathematicae
Volume	37
Issue number	3
DOIs	https://doi.org/10.1016/j.exmath.2018.01.001
State	Published - Sep 2019

Bibliographical note

Publisher Copyright:
© 2018 Elsevier GmbH

Funding

We are thankful to numerous people who read the preliminary version of this manuscript and shared their remarks and suggestions with us. This project would also be difficult to carry out without the generoussupport of the Israel Science Foundation (ISF) grant 953/13 (A.L.) and the National Science Foundation (NSF) grant DMS 080243 (F.N.).

Funders	Funder number
National Science Foundation	DMS 080243
Iowa Science Foundation	953/13
Israel Science Foundation
National Science Foundation

Keywords

Dyadic lattices
Singular integrals
Sparse families
Weighted bounds

Access to Document

10.1016/j.exmath.2018.01.001

Cite this

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Intuitive dyadic calculus: The basics

Abstract

Bibliographical note

Funding

Keywords

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