Positive Gaussian Kernels Also Have Gaussian Minimizers Rhonda S. Karg dispersion

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Positive Gaussian Kernels Also Have Gaussian Minimizers Rhonda S. Karg dispersionWe study lower bounds on multilinear operators with Gaussian kernels acting on Lebesgue spaces, with exponents below one. We put forward natural conditions when the optimal constant can be computed by inspecting centered Gaussian functions only, and we give necessary and sufficient conditions for this constant to be positive. Our work provides a counterpart to Lieb's results on maximizers of multilinear operators with real Gaussian kernels, also known