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On local properties of functions and singular integrals in terms of the mean oscillation

Rahim Rzaev, Lala Aliyeva (2008)

Open Mathematics

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.

On relations among the generalized second-order directional derivatives

Karel Pastor (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

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