We prove that if the composition operator F generated by a function f: [a, b] × ℝ → ℝ maps the space of bounded (p, k)-variation in the sense of Riesz-Popoviciu, p ≥ 1, k an integer, denoted by RV(p,k)[a, b], into itself and is uniformly bounded then RV(p,k)[a, b] satisfies the Matkowski condition.
@article{bwmeta1.element.doi-10_2478_s11533-012-0051-5,
author = {Francy Armao and Dorota G\l azowska and Sergio Rivas and Jessica Rojas},
title = {Uniformly bounded composition operators in the banach space of bounded (p, k)-variation in the sense of Riesz-Popoviciu},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {357-367},
zbl = {1296.47054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0051-5}
}
Francy Armao; Dorota Głazowska; Sergio Rivas; Jessica Rojas. Uniformly bounded composition operators in the banach space of bounded (p, k)-variation in the sense of Riesz-Popoviciu. Open Mathematics, Tome 11 (2013) pp. 357-367. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0051-5/
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