Multilinear measure theory and its applications

Abstract

The Grothendieck inequality and Grothendieck factorization theorem are fundamental tools in studying bimeasures. Motivated by Kwapien's theorem, we extend the Grothendieck inequality in a two-dimensional as well as a multidimensional framework.

Bimeasures appear naturally in the study of stochastic processes. We estimate the variations of bimeasures associated with a p-stable motion and a strongly stationary p-stable process. We also find analogues of these results for two-time processes and construct a p-stable motion.