Geodesic
Estimates of the derivatives of $n$-convex functions
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 24, Tome 232 (1996), pp. 123-133

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In terms of nonlinear norm estimates, a qualitative refinement of the following known result is obtained: on the class of $n$-convex functions, the $L^1$-convergence implies the $C^{(n-2)}$-convergence. Bibl. 2 titles. 
@article{ZNSL_1996_232_a9,
     author = {V. A. Malyshev},
     title = {Estimates of the derivatives of $n$-convex functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {123--133},
     publisher = {mathdoc},
     volume = {232},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_232_a9/}
}
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V. A. Malyshev. Estimates of the derivatives of $n$-convex functions. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 24, Tome 232 (1996), pp. 123-133. http://geodesic.mathdoc.fr/item/ZNSL_1996_232_a9/