The Composition Operator and the Space of the Functions of Bounded Variation in Schramm-Korenblum's Sense
We show that the composition operator H, associated with h:[a,b]→ℝ, maps the spaces Lip[a,b] on to the space κBVϕa,b of functions of bounded variation in Schramm-Korenblum's sense if and only if h is locally Lipschitz. Also, verify that if the composition operator generated by h:[a,b]×ℝ→ℝ maps...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/284389 |
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| _version_ | 1832553414077186048 |
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| author | Z. Jesús O. Mejía N. Merentes S. Rivas |
| author_facet | Z. Jesús O. Mejía N. Merentes S. Rivas |
| author_sort | Z. Jesús |
| collection | DOAJ |
| description | We show that the composition operator H, associated with h:[a,b]→ℝ, maps the spaces Lip[a,b] on to the space κBVϕa,b of functions of bounded variation in Schramm-Korenblum's sense if and only if h is locally Lipschitz. Also, verify that if the composition operator generated by h:[a,b]×ℝ→ℝ maps this space into itself and is uniformly bounded, then regularization of h is affine in the second variable. |
| format | Article |
| id | doaj-art-9c2e3e2696a449eba3b0a0d3abd893e3 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-9c2e3e2696a449eba3b0a0d3abd893e32025-02-03T05:54:05ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/284389284389The Composition Operator and the Space of the Functions of Bounded Variation in Schramm-Korenblum's SenseZ. Jesús0O. Mejía1N. Merentes2S. Rivas3Departamento de Matemática, Universidad Central de Venezuela, Caracas 1220A, VenezuelaDepartamento de Matemática, Universidad Central de Venezuela, Caracas 1220A, VenezuelaDepartamento de Matemática, Universidad Central de Venezuela, Caracas 1220A, VenezuelaInstituto Universitario Tecnológico Elías Calixto Pompa, Guatire, VenezuelaWe show that the composition operator H, associated with h:[a,b]→ℝ, maps the spaces Lip[a,b] on to the space κBVϕa,b of functions of bounded variation in Schramm-Korenblum's sense if and only if h is locally Lipschitz. Also, verify that if the composition operator generated by h:[a,b]×ℝ→ℝ maps this space into itself and is uniformly bounded, then regularization of h is affine in the second variable.http://dx.doi.org/10.1155/2013/284389 |
| spellingShingle | Z. Jesús O. Mejía N. Merentes S. Rivas The Composition Operator and the Space of the Functions of Bounded Variation in Schramm-Korenblum's Sense Journal of Function Spaces and Applications |
| title | The Composition Operator and the Space of the Functions of Bounded Variation in Schramm-Korenblum's Sense |
| title_full | The Composition Operator and the Space of the Functions of Bounded Variation in Schramm-Korenblum's Sense |
| title_fullStr | The Composition Operator and the Space of the Functions of Bounded Variation in Schramm-Korenblum's Sense |
| title_full_unstemmed | The Composition Operator and the Space of the Functions of Bounded Variation in Schramm-Korenblum's Sense |
| title_short | The Composition Operator and the Space of the Functions of Bounded Variation in Schramm-Korenblum's Sense |
| title_sort | composition operator and the space of the functions of bounded variation in schramm korenblum s sense |
| url | http://dx.doi.org/10.1155/2013/284389 |
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