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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

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

http://dx.doi.org/10.22199/issn.0717-6279-2020-05-0074 

Artículos

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

René Erlín Castillo1 
http://orcid.org/0000-0003-1113-5827

Héctor Camilo Chaparro2 
http://orcid.org/0000-0002-0723-8199

Eduard Trousselot3 

1Universidad Nacional de Colombia, Dept. de Matemáticas, Bogotá, Colombia e-mail: recastillo@unal.edu.co

2Universidad Militar Nueva Granada, Dept. de Matemáticas, Cajicá, Colombia e-mail: hector.chaparro@unimilitar.edu.co

3Universidad de Oriente, Departamento de Matemáticas, Cumaná, Venezuela e-mail: eddycharles2007@gmail.com

Abstract

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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Acknowledgments

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

References

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

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