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Littlewood-Paley theorem for Schroedinger operators

Shijun Zheng
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Abstract

Let $H$ be a Schrödinger operator on $\R^n$. 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 $L_p$ spaces as well as Sobolev 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.

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Shijun Zheng. 2006-09-06. Littlewood-Paley theorem for Schroedinger operators. https://arxiv.org/abs/math/0609185

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