Article citationsMore>>

J. Appell and P. P. Zabrejko, “Remarks on the Superposi- tion Operator Problem in Various Function Spaces,” Complex Variables and Elliptic Equations, Vol. 55, No. 8, 2010, pp. 727-737. doi:10.1080/17476930903568332

has been cited by the following article:

• 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