Sparse bounds for Bochner-Riesz multipliers

Maria Carmen Reguera, Michael Lacey, Dario Mena Arias

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
209 Downloads (Pure)

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

Keywords

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

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