Nemytskii operator on generalized bounded variation space

In this paper we show that if the Nemytskii operator maps the (φ, α)-bounded variation space into itself and satisfies some Lipschitz condition, then there are two functions g and h belonging to the (φ, α)-bounded variation space such that f(t, y) = g(t)y + h(t) for all t ∈ [a, b], y ∈ R....

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Main Authors:	René Erlín Castillo, Humberto Rafeiro, Eduard Trousselot
Format:	Article
Language:	Spanish
Published:	Universidad Industrial de Santander 2014-06-01
Series:	Revista Integración
Subjects:	Riesz p-variation α)-bounded variation p-variación de Riesz
Online Access:	http://revistas.uis.edu.co/index.php/revistaintegracion/article/view/4064/4410

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spelling	doaj-4d998173c1284934a3ad13a3d9a43d702020-11-24T23:18:52ZspaUniversidad Industrial de SantanderRevista Integración0120-419X2145-84722014-06-013217190Nemytskii operator on generalized bounded variation spaceRené Erlín Castillo0Humberto Rafeiro1Eduard Trousselot2Universidad Nacional de ColombiaPontificia Universidad JaverianaUniversidad de OrienteIn this paper we show that if the Nemytskii operator maps the (φ, α)-bounded variation space into itself and satisfies some Lipschitz condition, then there are two functions g and h belonging to the (φ, α)-bounded variation space such that f(t, y) = g(t)y + h(t) for all t ∈ [a, b], y ∈ R. Resumen. En este artículo demostramos que si el operador de Nemytskii lleva el espacio de variación (φ, α)-acotada en sí mismo, y satisface cierta condición de Lipschitz, entonces existen dos funciones g y h perteneciendo al espacio de variación (φ, α)-acotada tal que f(t, y) = g(t)y + h(t) para todo t ∈ [a, b], y ∈ R.http://revistas.uis.edu.co/index.php/revistaintegracion/article/view/4064/4410Riesz p-variationα)-bounded variationp-variación de Riesz
collection	DOAJ
language	Spanish
format	Article
sources	DOAJ
author	René Erlín Castillo Humberto Rafeiro Eduard Trousselot
spellingShingle	René Erlín Castillo Humberto Rafeiro Eduard Trousselot Nemytskii operator on generalized bounded variation space Revista Integración Riesz p-variation α)-bounded variation p-variación de Riesz
author_facet	René Erlín Castillo Humberto Rafeiro Eduard Trousselot
author_sort	René Erlín Castillo
title	Nemytskii operator on generalized bounded variation space
title_short	Nemytskii operator on generalized bounded variation space
title_full	Nemytskii operator on generalized bounded variation space
title_fullStr	Nemytskii operator on generalized bounded variation space
title_full_unstemmed	Nemytskii operator on generalized bounded variation space
title_sort	nemytskii operator on generalized bounded variation space
publisher	Universidad Industrial de Santander
series	Revista Integración
issn	0120-419X 2145-8472
publishDate	2014-06-01
description	In this paper we show that if the Nemytskii operator maps the (φ, α)-bounded variation space into itself and satisfies some Lipschitz condition, then there are two functions g and h belonging to the (φ, α)-bounded variation space such that f(t, y) = g(t)y + h(t) for all t ∈ [a, b], y ∈ R. Resumen. En este artículo demostramos que si el operador de Nemytskii lleva el espacio de variación (φ, α)-acotada en sí mismo, y satisface cierta condición de Lipschitz, entonces existen dos funciones g y h perteneciendo al espacio de variación (φ, α)-acotada tal que f(t, y) = g(t)y + h(t) para todo t ∈ [a, b], y ∈ R.
topic	Riesz p-variation α)-bounded variation p-variación de Riesz
url	http://revistas.uis.edu.co/index.php/revistaintegracion/article/view/4064/4410
work_keys_str_mv	AT reneerlincastillo nemytskiioperatorongeneralizedboundedvariationspace AT humbertorafeiro nemytskiioperatorongeneralizedboundedvariationspace AT eduardtrousselot nemytskiioperatorongeneralizedboundedvariationspace
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Nemytskii operator on generalized bounded variation space

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