Weighted norm inequalities of Bochner-Riesz means

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Abstract

Let w be a Muckenhoupt weight and Hwp (Rn) be the weighted Hardy spaces. We use the atomic decomposition of Hwp (Rn) and their molecular characters to show that the Bochner-Riesz means TRδ are bounded on Hwp (Rn) for 0 < p ≤ 1 and δ > max {n / p - (n + 1) / 2, [n / p] rw (rw - 1)-1 - (n + 1) / 2}, where rw is the critical index of w for the reverse Hölder condition. We also prove the Hwp - Lwp boundedness of the maximal Bochner-Riesz means T*δ for 0 < p ≤ 1 and δ > n / p - (n + 1) / 2.

Original languageEnglish
Pages (from-to)1274-1281
Number of pages8
JournalJournal of Mathematical Analysis and Applications
Volume324
Issue number2
DOIs
StatePublished - 15 Dec 2006

Keywords

  • A weights
  • Atomic decomposition
  • Bochner-Riesz means
  • Molecular characterization
  • Weighted Hardy spaces

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