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Modulated Energy Estimates for Singular Kernels and their Applications to Asymptotic Analyses for Kinetic Equations
.In this paper, we provide modulated interaction energy estimates for the kernel \(K(x) = |x|^{-\alpha }\) with \(\alpha \in (0,d)\) and its applications to quantified asymptotic analyses for kinetic equations. The proof relies on a dimension extension argument for an elliptic operator and its commutator estimates. For the applications, we …