Abstract
The Bochner–Riesz multipliers Bδ on Rn are shown to satisfy a range of sparse bounds, for all 0<δ<n−12 . The range of sparse bounds increases to the optimal range, as δ increases to the critical value, δ=n−12 , even assuming only partial information on the Bochner–Riesz conjecture in dimensions n≥3 . In dimension n=2 , we prove a sharp range of sparse bounds. The method of proof is based upon a ‘single scale’ analysis, and yields the sharpest known weighted estimates for the Bochner–Riesz multipliers in the category of Muckenhoupt weights.
Original language | English |
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Pages (from-to) | 1-15 |
Journal | Journal of Fourier Analysis and Applications |
Early online date | 30 Nov 2017 |
DOIs | |
Publication status | E-pub ahead of print - 30 Nov 2017 |
Keywords
- Bochner-Reisz
- multipliers
- sparse bounds
- weighted inequalities