Green's function asymptotics and sharp interpolation inequalities (Q2875026)

The authors study a general method to obtain sharp constants for the embeddings of the Sobolev spaces on an \(n\)-dimensional Riemannian manifold into the space of bounded continuous functions.NEWLINENEWLINE Their method is based on the study of the Green's function of an elliptic operator of order \(2m\), whose square root has domain determining the norm of the corresponding Sobolev space, precisely on the asymptotics with respect to the spectral parameter of the Green's function.NEWLINENEWLINE Moreover, an improvement of the well-known Carleson inequality is obtained.NEWLINENEWLINE In the first part of the paper, the authors describe a general method for finding sharp constants in some specific integral inequalities, including the inequalities with correction terms.NEWLINENEWLINE In the second part of the paper, they consider examples and applications of the general approach described in the first part.