Variational formulas of Poincaré-type inequalities in Banach spaces of functions on the line.
The author extends the variational formulas for (one-dimensional) Poin\-caré-type inequalities to the class of Banach function spaces. A particular attention is devoted to Orlicz spaces. He establishes explicit criteria for the inequalities to hold and explicit estimates of the optimal constants in the inequalities in question. As an application, the logarithmic Sobolev inequality is examined.
scientific article; zbMATH DE number 1885841