On Bounded Second Variation

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DOI: 10.4236/apm.2012.21005   PDF   HTML     3,965 Downloads   8,429 Views   Citations

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 Sg 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), A2p

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J. Giménez, L. López, N. Merentes and J. Sánchez, "On Bounded Second Variation," Advances in Pure Mathematics, Vol. 2 No. 1, 2012, pp. 22-26. doi: 10.4236/apm.2012.21005.

Conflicts of Interest

The authors declare no conflicts of interest.

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