On full derivatives
This paper is devoted to research on local properties of functions and multidimensional singular integrals in terms of their mean oscillation. The conditions guaranteeing existence of a derivative in the L p-sense at a given point are found. Spaces which remain invariant under singular integral operators are considered.
In the paper, we deal with the relations among several generalized second-order directional derivatives. The results partially solve the problem which of the second-order optimality conditions is more useful.