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EnglishIn 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 for the class of continuous H-convex functions in the Heisenberg group.
| Titolo: | On the second order derivatives of convex functions on the Heisenberg group |
| Autore/i: | C. E. GUTIRREZ; MONTANARI, ANNAMARIA |
| Autore/i Unibo: | |
| Anno: | 2004 |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.2422/2036-2145.2004.2.03 |
| Abstract: | 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 for the class of continuous H-convex functions in the Heisenberg group. |
| Data prodotto definitivo in UGOV: | 2005-09-23 17:46:30 |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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http://hdl.handle.net/11585/1898
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