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Interpolation Theorems For Self-Adjoint Operators, Shijun Zheng
Interpolation Theorems For Self-Adjoint Operators, Shijun Zheng
Department of Mathematical Sciences Faculty Publications
We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a self adjoint operator L, without assuming the gradient estimate for its spectral kernel. The result applies to the cases where L is a uniformly elliptic operator or a Schrödinger operator with electro-magnetic potential.
Harmonic Analysis Related To Schrödinger Operators, Gestur Olafsson, Shijun Zheng
Harmonic Analysis Related To Schrödinger Operators, Gestur Olafsson, Shijun Zheng
Department of Mathematical Sciences Faculty Publications
In this article, we give an overview of some recent developments in Littlewood-Paley theory for Schrödinger operators. We extend the Littlewood-Paley theory for special potentials considered in our previous work [J. Fourier Anal. Appl. 12 (2006), no. 6, 653–674; MR2275390]. We elaborate our approach by considering a potential in C∞0 or the Schwartz class in one dimension. In particular, the low energy estimates are treated by establishing some new and refined asymptotics for the eigenfunctions and their Fourier transforms. We give a maximal function characterization of the Besov spaces and Triebel-Lizorkin spaces associated with H. Then we …