# Sharp endpoint $$L^p$$ estimates for Schrödinger groups

@article{Chen2018SharpE, title={Sharp endpoint \$\$L^p\$\$ estimates for Schr{\"o}dinger groups}, author={Peng Chen and Xuan Thinh Duong and Ji Li and Lixin Yan}, journal={Mathematische Annalen}, year={2018} }

Let $L$ be a non-negative self-adjoint operator acting on $L^2(X)$ where $X$ is a space of homogeneous type with a dimension $n$. Suppose that the heat operator $e^{-tL}$ satisfies the generalized Gaussian $(p_0, p'_0)$-estimates of order $m$ for some $1\leq p_0 0$ independent of $t$ such that \begin{eqnarray*} \left\| (I+L)^{-{s}}e^{itL} f\right\|_{p} \leq C(1+|t|)^{s}\|f\|_{p}, \ \ \ t\in{\mathbb R}, \ \ \ s= n\big|{1\over 2}-{1\over p}\big|. \end{eqnarray*} As a consequence, the above…

## 10 Citations

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