TITLE:
On Bounded Second Variation
AUTHORS:
José Giménez, Lorena López, N. Merentes, J. L. Sánchez
KEYWORDS:
Function of Bounded Variation; Lipschitz Continuous Function; Absolutely Continuous Function; Nemytskij Operator
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.2 No.1,
January
9,
2012
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