Sharp Gaussian estimates for Schrödinger heat kernels: $L^p$ integrability conditions

preprint2016arXivOpen access

We give new sufficient conditions for comparability of the fundamental solution of the Schrödinger equation $\partial_t=Δ+V$ 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 Schrödinger heat kernels: $L^p$ integrability conditions

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Sharp Gaussian estimates for Schrödinger heat kernels: LpL^pLp integrability conditions

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Sharp Gaussian estimates for Schrödinger heat kernels: $L^p$ integrability conditions