On the sense of convergence in the dyadic representation theorem

2023/12/31 by Hytönen, Tuomas
#42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.00491

Abstract

The dyadic representation of any singular integral operator, as an average of dyadic model operators, has found many applications. While for many purposes it is enough to have such a representation for a "suitable class" of test functions, we show that, under quite general assumptions (essentially minimal ones to make sense of the formula), the representation is actually valid for all pairs (f,g)∈ L^p(\mathbb R^d)× L^p'(\mathbb R^d), not just test functions.

Related

• Perfect dyadic operators: weighted T(1) theorem and two weight estimates
• Uniform sparse domination of singular integrals via dyadic shifts
• Global Rational Approximations of Functions With Factorially Divergent Asymptotic Series
• Kotlarski's lemma for dyadic models
• The dyadic Riesz vector II