Operator-valued Fourier multipliers on toroidal Besov spaces
We prove in this paper that a sequence M: Zn → L(E) of bounded variation is a Fourier multiplier on the Besov space Bsp, q(Tn, E) for s ∈ R, 1 p ∞, 1 ≤ q ≤ ∞ and E a Banach space, if and only if E is a UMD-space. This extends the Theorem 4.2 in [3] to the n-dimensional case. As illustration of the a...
- Autores:
-
Barraza Martínez, Bienvenido
González Martínez, Iván
Hernández Monzón, Jairo
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2016
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/66457
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/66457
http://bdigital.unal.edu.co/67485/
- Palabra clave:
- 51 Matemáticas / Mathematics
Fourier multipliers
operator-valued symbols
UMD- spaces
toroidal Besov spaces
Multiplicadores de Fourier
símbolos operador-valuados
espacios UMD
espacios de Besov toroidales.
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Barraza Martínez, Bienvenidob9c76af7-6a13-4e38-bda1-c0adf2408d9d300González Martínez, Iván6118734b-4e0b-4e4c-9c6a-f660031f8c1c300Hernández Monzón, Jairo6ec02f73-77b2-4001-9b03-a45d7d16a0093002019-07-03T02:09:51Z2019-07-03T02:09:51Z2016-01-01ISSN: 2357-4100https://repositorio.unal.edu.co/handle/unal/66457http://bdigital.unal.edu.co/67485/We prove in this paper that a sequence M: Zn → L(E) of bounded variation is a Fourier multiplier on the Besov space Bsp, q(Tn, E) for s ∈ R, 1 p ∞, 1 ≤ q ≤ ∞ and E a Banach space, if and only if E is a UMD-space. This extends the Theorem 4.2 in [3] to the n-dimensional case. As illustration of the applicability of this results we study the solvability of two abstract Cauchy problems with periodic boundary conditions.En el presente artículo se prueba que una sucesión M: Zn → L(E) de variación acotada, es un multiplicador de Fourier sobre el espacio de Besov Bsp, q(Tn, E) para s ∈ R, 1 p ∞, 1 ≤ q ≤ 1 y E un espacio de Banach, si y solo si, E es un espacio UMD. Este resultado extiende el Teorema 4.2 en [3] al caso n-dimensional. Como ilustración de la aplicabilidad de este resultado, se estudia la solubilidad de dos problemas de Cauchy abstractos con condiciones de frontera periódicas.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticashttps://revistas.unal.edu.co/index.php/recolma/article/view/62205Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasBarraza Martínez, Bienvenido and González Martínez, Iván and Hernández Monzón, Jairo (2016) Operator-valued Fourier multipliers on toroidal Besov spaces. Revista Colombiana de Matemáticas, 50 (1). pp. 109-137. ISSN 2357-410051 Matemáticas / MathematicsFourier multipliersoperator-valued symbolsUMD- spacestoroidal Besov spacesMultiplicadores de Fouriersímbolos operador-valuadosespacios UMDespacios de Besov toroidales.Operator-valued Fourier multipliers on toroidal Besov spacesArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL62205-316266-1-SM.pdfapplication/pdf518980https://repositorio.unal.edu.co/bitstream/unal/66457/1/62205-316266-1-SM.pdfa6820843a00bd9399f0c811a8d880c97MD51THUMBNAIL62205-316266-1-SM.pdf.jpg62205-316266-1-SM.pdf.jpgGenerated Thumbnailimage/jpeg4795https://repositorio.unal.edu.co/bitstream/unal/66457/2/62205-316266-1-SM.pdf.jpgbf2fe9cc4ae5b4b385d7ab47081471d2MD52unal/66457oai:repositorio.unal.edu.co:unal/664572023-05-25 23:02:46.727Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |
| dc.title.spa.fl_str_mv |
Operator-valued Fourier multipliers on toroidal Besov spaces |
| title |
Operator-valued Fourier multipliers on toroidal Besov spaces |
| spellingShingle |
Operator-valued Fourier multipliers on toroidal Besov spaces 51 Matemáticas / Mathematics Fourier multipliers operator-valued symbols UMD- spaces toroidal Besov spaces Multiplicadores de Fourier símbolos operador-valuados espacios UMD espacios de Besov toroidales. |
| title_short |
Operator-valued Fourier multipliers on toroidal Besov spaces |
| title_full |
Operator-valued Fourier multipliers on toroidal Besov spaces |
| title_fullStr |
Operator-valued Fourier multipliers on toroidal Besov spaces |
| title_full_unstemmed |
Operator-valued Fourier multipliers on toroidal Besov spaces |
| title_sort |
Operator-valued Fourier multipliers on toroidal Besov spaces |
| dc.creator.fl_str_mv |
Barraza Martínez, Bienvenido González Martínez, Iván Hernández Monzón, Jairo |
| dc.contributor.author.spa.fl_str_mv |
Barraza Martínez, Bienvenido González Martínez, Iván Hernández Monzón, Jairo |
| dc.subject.ddc.spa.fl_str_mv |
51 Matemáticas / Mathematics |
| topic |
51 Matemáticas / Mathematics Fourier multipliers operator-valued symbols UMD- spaces toroidal Besov spaces Multiplicadores de Fourier símbolos operador-valuados espacios UMD espacios de Besov toroidales. |
| dc.subject.proposal.spa.fl_str_mv |
Fourier multipliers operator-valued symbols UMD- spaces toroidal Besov spaces Multiplicadores de Fourier símbolos operador-valuados espacios UMD espacios de Besov toroidales. |
| description |
We prove in this paper that a sequence M: Zn → L(E) of bounded variation is a Fourier multiplier on the Besov space Bsp, q(Tn, E) for s ∈ R, 1 p ∞, 1 ≤ q ≤ ∞ and E a Banach space, if and only if E is a UMD-space. This extends the Theorem 4.2 in [3] to the n-dimensional case. As illustration of the applicability of this results we study the solvability of two abstract Cauchy problems with periodic boundary conditions. |
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2016 |
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2016-01-01 |
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2019-07-03T02:09:51Z |
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2019-07-03T02:09:51Z |
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Artículo de revista |
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ISSN: 2357-4100 |
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https://repositorio.unal.edu.co/handle/unal/66457 |
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ISSN: 2357-4100 |
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spa |
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https://revistas.unal.edu.co/index.php/recolma/article/view/62205 |
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Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas Revista Colombiana de Matemáticas |
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Barraza Martínez, Bienvenido and González Martínez, Iván and Hernández Monzón, Jairo (2016) Operator-valued Fourier multipliers on toroidal Besov spaces. Revista Colombiana de Matemáticas, 50 (1). pp. 109-137. ISSN 2357-4100 |
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Derechos reservados - Universidad Nacional de Colombia |
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Atribución-NoComercial 4.0 Internacional |
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info:eu-repo/semantics/openAccess |
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