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arXiv · 2509.09491

The optimal bound $e$ in a dyadic version of Uchiyama's Lemma

J. Fladung·S. Petermichl
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Abstract

The best known constant in Uchiyama's Lemma is $e$. A conjecture states that this cannot be improved. We show that the constant $e$ also stands in a dyadic version of Uchiyama's Lemma. Further, we prove that in the dyadic case, the constant $e$ can indeed not be improved. We deduce a dyadic version of the reproducing kernel thesis for the embedding theorem.

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J. Fladung, S. Petermichl. 2025-09-11. The optimal bound $e$ in a dyadic version of Uchiyama's Lemma. https://arxiv.org/abs/2509.09491

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