Hessian measures in the class of m-convex (m - cv) functions

Abstract

The theory of m-convex (m − cv) functions is a new direction in the real geometry. In this work, by using the connection m − cv functions with strongly m-subharmonic (shm) functions and using well-known and rich properties of shm functions, we show a number of important properties of the class of m−cv functions, in particular, we study Hessians Hk(u), k = 1, 2, ..., n − m +1, in the class of bounded m − cv functions.

Keywords

• Convex function
• m-convex function
• Strongly m-subharmonic function
• Borel measures
• Hessians