instituto de matemáticas universidad de sevilla
Antonio de Castro Brzezicki
Sharp affine Sobolev type inequalities and the Busemann-Petty centroid inequality
We show that the Lp Busemann-Petty centroid inequality for convex sets provides an elementary proof of many affine-invariant functional inequalities in a unified approach. The inequalities are Sharp and the extremal functions are characterized in most of the cases.