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Analysis on Flag Manifolds and Sobolev Inequalities

  • Bent Ørsted
Chapter
Part of the Progress in Mathematics book series (PM, volume 306)

Abstract

Analysis on flag manifolds GP has connections to both representation theory and geometry; in this paper we show how one may derive some new Sobolev inequalities on spheres by combining rearrangement inequalities with analysis of principal series representations of rank-one semisimple Lie groups. In particular the Sobolev inequalities obtained involve hypoelliptic differential operators as opposed to elliptic ones in the usual case. One may hope that these ideas might in some form be extended to other parabolic geometries as well.

Keywords

Sobolev inequalities Parabolic geometry Principal series representations 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Matematisk InstitutAarhus CDenmark

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