End Point Estimate of Littlewood-Paley Operator Associated to the Generalized Schrödinger Operator - Yanping Chen; Wenyu Tao (Journal of Function Spaces)
Let L=−Δ+μ be the generalized Schrödinger operator on ℝd,d≥3, where μ≠0 is a nonnegative Radon measure satisfying certain scale-invariant Kato conditions and doubling conditions. In this work, we give a new BMO space associated to the generalized Schrödinger operator L,BMOθ,L, which is bigger than the BMO spaces related to the classical Schrödinger operators A=−Δ+V, with V a potential satisfying a reverse Hölder inequality introduced by Dziubański et al. in 2005. Besides, the boundedness of the Littlewood-Paley operators associated to L in BMOθ,L also be proved.