Bilinear operators associated with Schrödinger operators

Chin Cheng Lin, Ying Chieh Lin, Heping Liu, Yu Liu

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Let L = -Δ +V be a Schrödinger operator in ℝd and HL1(ℝd) be the Hardy type space associated to L. We investigate the bilinear operators T+ and T - defined by T±(f,g)(x) = (T1f)(x) (T2g)(x) ± (T2f)(x)(T1g)(x), where T1 and T2 are Calderón-Zygmund operators related to L. Under some general conditions, we prove that either T+ or T - is bounded from Lp(ℝ) × Lq(ℝ d) to HL1(ℝd) for 1 < p, q < ∞ with 1/p + 1/q = 1. Several examples satisfying these conditions are given. We also give a counterexample for which the classical Hardy space estimate fails.

Original languageEnglish
Pages (from-to)281-295
Number of pages15
JournalStudia Mathematica
Volume205
Issue number3
DOIs
StatePublished - 2011

Keywords

  • Bilinear operators
  • Hardy spaces
  • Riesz transforms
  • Schrödinger operators

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