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On Bounded Second Variation

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DOI: 10.4236/apm.2012.21005    3,822 Downloads   8,208 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

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

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