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The dyadic representation of any singular integral operator, as an average ofdyadic model operators, has found many applications. While for many purposes itis enough to have such a representation for a "suitable class" of testfunctions, we show that, under quite general assumptions (essentially minimalones to make sense of the formula), the representation is actually valid forall pairs $(f,g)\in L^p(\mathbb R^d)\times L^{p'}(\mathbb R^d)$, not just testfunctions.

On the sense of convergence in the dyadic representation theorem