INTERSECTION BODIES AND Lp-SPACES

In this talk we discuss a new connection between convex geometry and the theory of Lp-spaces. It appears that intersection bodies, one the main objects of convex geometry, are directly related to the concept of embedding of normed spaces in Lp with p < 0. This allows to get new geometric results by extending different facts about Lp-spaces to negative values of p. We present several applications of this approach. In particular, in joint work with N.Kalton, the factorization theorem of Maurey and Nikishin was extended to negative p, which implies that intersection bodies are isomorphically equivalent to subspaces of Lq for each 0 < q < 1. Department of Mathematics, University of Missouri, Columbia, MO 65211. E-mail address: [email protected]