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過去の記録 ～04/26｜次回の予定｜今後の予定 04/27～
| 開催情報 | 木曜日 16:00～17:30 数理科学研究科棟(駒場) 号室 |
|---|---|
| 担当者 | 石毛 和弘，宮本 安人，Neal Bez，高田 了 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/seminar/applana/index.html |
2026年06月04日(木)
16:00-17:30 数理科学研究科棟(駒場) 002号室
白木 尚武 氏 (University of Zagreb)
Beckner's sharp inequalities revisited on binary cubes (Japanese)
白木 尚武 氏 (University of Zagreb)
Beckner's sharp inequalities revisited on binary cubes (Japanese)
[ 講演概要 ]
The Hausdorff–Young inequality and Young’s convolution inequality are fundamental tools in harmonic analysis. The landmark paper “Inequalities in Fourier Analysis” by William Beckner (Ann. of Math., 1975) established the exact values of the sharp constants appearing in these inequalities. Recently, these inequalities have received renewed attention in the setting of binary cubes, driven by applications in additive combinatorics through works by Kane–Tao, de Dios Pont–Greenfeld–Ivanisvili–Madrid, and others. In this discrete setting, the sharp constant is known to be 1 and is no longer the central issue. Instead, the focus shifts to the range of exponents for which the Hausdorff–Young inequality and Young’s convolution inequality hold — a range that is enlarged compared to the classical case. In this talk, we aim to fully characterize this range. This is joint work with Tonći Crmarić (University of Split) and Vjekoslav Kovač (University of Zagreb).
The Hausdorff–Young inequality and Young’s convolution inequality are fundamental tools in harmonic analysis. The landmark paper “Inequalities in Fourier Analysis” by William Beckner (Ann. of Math., 1975) established the exact values of the sharp constants appearing in these inequalities. Recently, these inequalities have received renewed attention in the setting of binary cubes, driven by applications in additive combinatorics through works by Kane–Tao, de Dios Pont–Greenfeld–Ivanisvili–Madrid, and others. In this discrete setting, the sharp constant is known to be 1 and is no longer the central issue. Instead, the focus shifts to the range of exponents for which the Hausdorff–Young inequality and Young’s convolution inequality hold — a range that is enlarged compared to the classical case. In this talk, we aim to fully characterize this range. This is joint work with Tonći Crmarić (University of Split) and Vjekoslav Kovač (University of Zagreb).
