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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.39 no.5 Antofagasta  2020 


On functions of (ϕ, 2, α)-bounded variation

René Erlín Castillo1

Héctor Camilo Chaparro2

Eduard Trousselot3 

1Universidad Nacional de Colombia, Dept. de Matemáticas, Bogotá, Colombia e-mail:

2Universidad Militar Nueva Granada, Dept. de Matemáticas, Cajicá, Colombia e-mail:

3Universidad de Oriente, Departamento de Matemáticas, Cumaná, Venezuela e-mail:


We introduce the (ϕ, 2, α)-bounded variation spaces, which are a common generalization between Riesz’s spaces, p-variation and (ϕ, 2)-bounded variation spaces. We also study its structure as Banach spaces, as well as some embedding results.

Keywords: Riesz p-variation; (ϕ, 2)-bounded variation; Bounded variation

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H. C. Chaparro was supported by Research Office UMNG through the project INV-CIAS-3151.


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Received: July 31, 2019; Accepted: August 31, 2019

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