The k-stein condition on Damek-Ricci spaces

DRUETTA MARIA J.

Proceedings of the Conference on Contemporary Geometry and Related Topics

Proceedings of the Conference, University of Belgrado, Serbia

Lugar: Belgrado; Año: 2006 vol. 1 p. 205 - 215

We study the k-stein condition on Damek-Ricci spaces S: these spaces are Einstein (1-stein) and 2-stein . We show that  if  S satisfies the k-stein condition  for some k>0  then k= 1, 2 or 3. In the later case S is a symmetric space of noncompact type and rank one and S is k-stein for all natural k>0. Equivalently, Damek-Ricci spaces are not k-stein for any k>2, unless they are symmetric.