Littlewood-Paley Theorem for Schrödinger Operators
Analysis in Theory and Applications
Let H be a Schrödinger operator on ℝn. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.
"Littlewood-Paley Theorem for Schrödinger Operators."
Analysis in Theory and Applications, 22 (4): 353-361.