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Intuitive dyadic calculus: The basics

Institution:	1. Department of Mathematics, Indian Institute of Science Education and Research, Mohali, India;2. Department of Mathematics, Indian Institute of Science Education and Research Bhopal, Bhopal-462066, India;1. Department of Mathematics, University of Missouri, Columbia MO 65211, USA;2. Department of Mathematics, Sun Yat-sen (Zhongshan) University, Guangzhou, Guangdong, China;3. Department of Mathematics, Charles University, 116 36 Praha 1, Czech Republic;1. Center for Applied Mathematics, Tianjin University, Weijin Road 92, 300072 Tianjin, China;2. Department of Mathematics and Statistics, University of Helsinki, P.O.B. 68, FI-00014 University of Helsinki, Finland

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.

Keywords:	Dyadic lattices Sparse families Singular integrals Weighted bounds
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