On Bounded Second Variation ()
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
Share and Cite:
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.