Sharp Inequalities for Heat Kernels of Schrِdinger Operators and Applications to Spectral Gaps

This paper derives inequalities for multiple integrals from which sharp inequalities for ratios of heat kernels and integrals of heat kernels of certain Schrödinger operators follow. Such ratio inequalities imply sharp inequalities for spectral gaps. The multiple integral inequalities, although very different, are motivated by the now classical Brascamp–Lieb–Luttinger rearrangement inequalities.