T1 criterions for generalised Calderón--Zygmund type operators on Hardy and BMO spaces associated to Schrödinger operators and applications

2015/10/09 by Bui, The Anh, Li, Ji, Ly, Fu Ken
#35J10 #42B20 #42B30 #42B35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.02531

Abstract

Suppose L=-Δ+V is a Schrödinger operator on ℝⁿ with a potential V belonging to certain reverse Hölder class RH_σ with σ≥ n/2. The main aim of this paper is to provide necessary and sufficient conditions in terms of T1 criteria for a generalised Calderón--Zygmund type operator with respect to L to be bounded on Hardy spaces H^p_L(ℝⁿ) and on BMO type spaces BMO_L^α(ℝⁿ) associated with L. As applications, we prove the boundedness for several singular integral operators associated to L. Our approach is flexible enough to prove the boundedness of the Riesz transforms related to L with n/2 ≤ σ

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