On Bounded Second Variation

José Giménez, Lorena López, N. Merentes, J. L. Sánchez

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DOI: 10.4236/apm.2012.21005                

Abstract

In this paper, we discuss various aspects of the problem of space-invariance, under compositions, of certain subclasses of the space of all continuously differentiable functions on an interval [a,b] We present a result about integrability of products of the form gοf.f^'f^(k)under suitable mild conditions and, finally, we prove that a Nemytskij operator S_g maps BV^''[a,b] a distinguished subspace of the space of all functions of second bounded variation, into itself if, and only if, g BV^''_loc(R) A similar result is obtained for the space of all functions of bounded (p,2)-variation (1≤p≤1), A²_p

Keywords

Function of Bounded Variation; Lipschitz Continuous Function; Absolutely Continuous Function; Nemytskij Operator

Conflicts of Interest

The authors declare no conflicts of interest.

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