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Applied Analysis
Seminar information archive ～04/26｜Next seminar｜Future seminars 04/27～
| Date, time & place | Thursday 16:00 - 17:30 Room # (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kazuhiro Ishige, Yasuhito Miyamoto, Neal Bez, Ryo Takada |
2026/06/04
16:00-17:30 Room # 002 (Graduate School of Math. Sci. Bldg.)
Shobu Shiraki (University of Zagreb)
Beckner's sharp inequalities revisited on binary cubes (Japanese)
Shobu Shiraki (University of Zagreb)
Beckner's sharp inequalities revisited on binary cubes (Japanese)
[ Abstract ]
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).
