Displaying similar documents to “Regularity of convex functions on Heisenberg groups”

On the second order derivatives of convex functions on the Heisenberg group

Cristian E. Gutiérrez, Annamaria Montanari (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In the euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex functions are a.e. twice differentiable. In this paper we prove that a similar result holds in the Heisenberg group, by showing that every continuous ℋ –convex function belongs to the class of functions whose second order horizontal distributional derivatives are Radon measures. Together with a recent result by Ambrosio and Magnani, this proves the existence a.e. of second order horizontal derivatives...

Pairs of sets with convex union.

Ryszard Urbanski (1997)

Collectanea Mathematica

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In this paper the notion of convex pairs of convex bounded subsets of a Hausdorff topological vector space is introduced. Criteria of convexity pair are proved.

The Space of Differences of Convex Functions on [0, 1]

Zippin, M. (2000)

Serdica Mathematical Journal

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∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany). The space K[0, 1] of differences of convex functions on the closed interval [0, 1] is investigated as a dual Banach space. It is proved that a continuous function f on [0, 1] belongs to K[0, 1] ...

A Clarke–Ledyaev Type Inequality for Certain Non–Convex Sets

Ivanov, M., Zlateva, N. (2000)

Serdica Mathematical Journal

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We consider the question whether the assumption of convexity of the set involved in Clarke-Ledyaev inequality can be relaxed. In the case when the point is outside the convex hull of the set we show that Clarke-Ledyaev type inequality holds if and only if there is certain geometrical relation between the point and the set.