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arXiv · 2401.00491

On the sense of convergence in the dyadic representation theorem

Tuomas Hytönen
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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 $(f,g)\in L^p(\mathbb R^d)\times L^{p'}(\mathbb R^d)$, not just test functions.

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Tuomas Hytönen. 2023-12-31. On the sense of convergence in the dyadic representation theorem. https://arxiv.org/abs/2401.00491

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