Multi-Linear Interpolation Of Restricted Type Estimates Reduced By Strong L~p Estimates

In this paper,the relevant properties of the structures on convex polyhedrons associated to permutations in R~n,n∈N,n≥3 are explained,and a series of general multi-linear interpo-lation theorems which allow one to obtain restricted type estimates for a large set of exponents are given.Moreover,some errors in Ref.[19]are pointed out and an application for 3-linear form is also presented.