Sparse bounds for Bochner-Riesz multipliers

Research output: Contribution to journalArticle

Authors

Colleges, School and Institutes

External organisations

  • Georgia Institute of Technology, Atlanta, Georgia, USA.

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.

Details

Original languageEnglish
Pages (from-to)1-15
JournalJournal of Fourier Analysis and Applications
Early online date30 Nov 2017
Publication statusE-pub ahead of print - 30 Nov 2017

Keywords

  • Bochner-Reisz , multipliers , sparse bounds , weighted inequalities