In this paper, we develop the weighted energy estimates for arbitrary 4-convex vectors and the vectors having both 4-convex and 4-concave functions as their arguments. To do this, we first develop these estimates for smooth 4-convex vectors and then, through mollification, extend the results for arbitrary 4-convex vectors. This type of estimates are valuable in problems of financial mathematics for the establishment of optimal investment strategies
Smooth convex vectors, smooth concave vectors, vector convolution
SALEEM, MUHAMMAD SHOAIB; PECARIC, JOSIP; REHMAN, HAMOOD UR; MUNIR, MOBEEN; and KHAN, MUHAMMAD WAHAB
"If $4$-convex vectors are closed in uniform norms then their second derivatives are also closed in weighted $L^2$-norm,"
Turkish Journal of Mathematics: Vol. 42:
5, Article 2.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss5/2