Lp boundedness of commutators of Riesz transforms associated to Schrödinger operator

Zihua Guo, Pengtao Li, Lizhong Peng

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51 Citations (Scopus)

Abstract

In this paper we consider Lp boundedness of some commutators of Riesz transforms associated to Schrödinger operator P = - Δ + V (x) on Rn, n ≥ 3. We assume that V (x) is non-zero, non-negative, and belongs to Bq for some q ≥ n / 2. Let T1 = (- Δ + V)-1 V, T2 = (- Δ + V)- 1 / 2 V1 / 2 and T3 = (- Δ + V)- 1 / 2 ∇. We obtain that [b, Tj](j = 1, 2, 3) are bounded operators on Lp (Rn) when p ranges in a interval, where b ∈ BMO (Rn). Note that the kernel of Tj(j = 1, 2, 3) has no smoothness.

Original languageEnglish
Pages (from-to)421-432
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume341
Issue number1
DOIs
Publication statusPublished - 1 May 2008
Externally publishedYes

Keywords

  • BMO
  • Boundedness
  • Commutator
  • Riesz transforms associated to Schrödinger operators
  • Smoothness

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