Subcritical approach to conformally invariant extension operators on the upper half space

Abstract

In this work we obtain sharp embedding inequalities for a family of conformally invariant integral extension operators. This family includes (among others) the classical Poisson extension operator and the extension operator with Riesz kernel. We show that the sharp constants in these inequalities are attained and classify the corresponding extremal functions. We also compute the limiting behavior at the boundary of the extensions of the extremal functions.