The optimal bound $e$ in a dyadic version of Uchiyama's Lemma
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911150179876864 |
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| author | Fladung, J. Petermichl, S. |
| author_facet | Fladung, J. Petermichl, S. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_09491 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The optimal bound $e$ in a dyadic version of Uchiyama's Lemma Fladung, J. Petermichl, S. Classical Analysis and ODEs 42B20, 60G42, 60G46, 30D55, 42B30, 46E22 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. |
| title | The optimal bound $e$ in a dyadic version of Uchiyama's Lemma |
| topic | Classical Analysis and ODEs 42B20, 60G42, 60G46, 30D55, 42B30, 46E22 |
| url | https://arxiv.org/abs/2509.09491 |