Sharp Gaussian estimates for Schr\"odinger heat kernels: $L^p$ integrability conditions

Jacek Dziuba\'nski; Karol Szczypkowski; Krzysztof Bogdan

arxiv: 1511.07167 · v3 · pith:U2G2VQYNnew · submitted 2015-11-23 · 🧮 math.FA · math.AP

Sharp Gaussian estimates for Schr\"odinger heat kernels: L^p integrability conditions

Krzysztof Bogdan , Jacek Dziuba\'nski , Karol Szczypkowski This is my paper

classification 🧮 math.FA math.AP

keywords comparabilityconditionsintegrabilityodingerschrdeltaequationestimates

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We give new sufficient conditions for comparability of the fundamental solution of the Schr\"odinger equation $\partial_t=\Delta+V$ with the Gauss-Weierstrass kernel and show that local $L^p$ integrability of $V$ for $p> 1$ is not necessary for the comparability.

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Sharp Gaussian estimates for Schr\"odinger heat kernels: L^p integrability conditions

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