Weighted inequalities for Hardy-Steklov operators
- Autores
- Bernardis, Ana Lucia; Martín Reyes, Francisco Javier; Salvador, P. Ortega
- Año de publicación
- 2007
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We characterize the pairs of weights (v, w) for which the operator Tf(x) = g(x) ∫s(x)h(x) f with s and h increasing and continuous functions is of strong type (p, q) or weak type (p, q) with respect to the pair (v, w) in the case 0 < q < p and 1 < p < ∞. The result for the weak type is new while the characterizations for the strong type improve the ones given by H. P. Heinig and G. Sinnamon, In particular, we do not assume differentiability properties on s and h and we obtain that the strong type inequality (p, q), q < p, is characterized by the fact that the function Φ(x) = sup (∫cd gqw) 1/p (∫s(d)h(c) v1-p′) 1/p′ belongs to Lr(gqw), where 1/r = 1/q - 1/q and the supremum is taken over all c and d such that c ≤ x ≤ d and s(d) ≤ h(c).
Fil: Bernardis, Ana Lucia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Martín Reyes, Francisco Javier. Universidad de Málaga; España
Fil: Salvador, P. Ortega. Universidad de Málaga; España - Materia
-
HARDY-STEKLOV OPERATOR
INEQUALITIES
WEIGHTS - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/84239
Ver los metadatos del registro completo
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Weighted inequalities for Hardy-Steklov operatorsBernardis, Ana LuciaMartín Reyes, Francisco JavierSalvador, P. OrtegaHARDY-STEKLOV OPERATORINEQUALITIESWEIGHTShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We characterize the pairs of weights (v, w) for which the operator Tf(x) = g(x) ∫s(x)h(x) f with s and h increasing and continuous functions is of strong type (p, q) or weak type (p, q) with respect to the pair (v, w) in the case 0 < q < p and 1 < p < ∞. The result for the weak type is new while the characterizations for the strong type improve the ones given by H. P. Heinig and G. Sinnamon, In particular, we do not assume differentiability properties on s and h and we obtain that the strong type inequality (p, q), q < p, is characterized by the fact that the function Φ(x) = sup (∫cd gqw) 1/p (∫s(d)h(c) v1-p′) 1/p′ belongs to Lr(gqw), where 1/r = 1/q - 1/q and the supremum is taken over all c and d such that c ≤ x ≤ d and s(d) ≤ h(c).Fil: Bernardis, Ana Lucia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Martín Reyes, Francisco Javier. Universidad de Málaga; EspañaFil: Salvador, P. Ortega. Universidad de Málaga; EspañaCanadian Mathematical Soc2007-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/84239Bernardis, Ana Lucia; Martín Reyes, Francisco Javier; Salvador, P. Ortega; Weighted inequalities for Hardy-Steklov operators; Canadian Mathematical Soc; Canadian Journal Of Mathematics; 59; 2; 12-2007; 276-2950008-414XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.4153/CJM-2007-011-xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:05:06Zoai:ri.conicet.gov.ar:11336/84239instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:05:06.919CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
Weighted inequalities for Hardy-Steklov operators |
| title |
Weighted inequalities for Hardy-Steklov operators |
| spellingShingle |
Weighted inequalities for Hardy-Steklov operators Bernardis, Ana Lucia HARDY-STEKLOV OPERATOR INEQUALITIES WEIGHTS |
| title_short |
Weighted inequalities for Hardy-Steklov operators |
| title_full |
Weighted inequalities for Hardy-Steklov operators |
| title_fullStr |
Weighted inequalities for Hardy-Steklov operators |
| title_full_unstemmed |
Weighted inequalities for Hardy-Steklov operators |
| title_sort |
Weighted inequalities for Hardy-Steklov operators |
| dc.creator.none.fl_str_mv |
Bernardis, Ana Lucia Martín Reyes, Francisco Javier Salvador, P. Ortega |
| author |
Bernardis, Ana Lucia |
| author_facet |
Bernardis, Ana Lucia Martín Reyes, Francisco Javier Salvador, P. Ortega |
| author_role |
author |
| author2 |
Martín Reyes, Francisco Javier Salvador, P. Ortega |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
HARDY-STEKLOV OPERATOR INEQUALITIES WEIGHTS |
| topic |
HARDY-STEKLOV OPERATOR INEQUALITIES WEIGHTS |
| purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| dc.description.none.fl_txt_mv |
We characterize the pairs of weights (v, w) for which the operator Tf(x) = g(x) ∫s(x)h(x) f with s and h increasing and continuous functions is of strong type (p, q) or weak type (p, q) with respect to the pair (v, w) in the case 0 < q < p and 1 < p < ∞. The result for the weak type is new while the characterizations for the strong type improve the ones given by H. P. Heinig and G. Sinnamon, In particular, we do not assume differentiability properties on s and h and we obtain that the strong type inequality (p, q), q < p, is characterized by the fact that the function Φ(x) = sup (∫cd gqw) 1/p (∫s(d)h(c) v1-p′) 1/p′ belongs to Lr(gqw), where 1/r = 1/q - 1/q and the supremum is taken over all c and d such that c ≤ x ≤ d and s(d) ≤ h(c). Fil: Bernardis, Ana Lucia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina Fil: Martín Reyes, Francisco Javier. Universidad de Málaga; España Fil: Salvador, P. Ortega. Universidad de Málaga; España |
| description |
We characterize the pairs of weights (v, w) for which the operator Tf(x) = g(x) ∫s(x)h(x) f with s and h increasing and continuous functions is of strong type (p, q) or weak type (p, q) with respect to the pair (v, w) in the case 0 < q < p and 1 < p < ∞. The result for the weak type is new while the characterizations for the strong type improve the ones given by H. P. Heinig and G. Sinnamon, In particular, we do not assume differentiability properties on s and h and we obtain that the strong type inequality (p, q), q < p, is characterized by the fact that the function Φ(x) = sup (∫cd gqw) 1/p (∫s(d)h(c) v1-p′) 1/p′ belongs to Lr(gqw), where 1/r = 1/q - 1/q and the supremum is taken over all c and d such that c ≤ x ≤ d and s(d) ≤ h(c). |
| publishDate |
2007 |
| dc.date.none.fl_str_mv |
2007-12 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/84239 Bernardis, Ana Lucia; Martín Reyes, Francisco Javier; Salvador, P. Ortega; Weighted inequalities for Hardy-Steklov operators; Canadian Mathematical Soc; Canadian Journal Of Mathematics; 59; 2; 12-2007; 276-295 0008-414X CONICET Digital CONICET |
| url |
http://hdl.handle.net/11336/84239 |
| identifier_str_mv |
Bernardis, Ana Lucia; Martín Reyes, Francisco Javier; Salvador, P. Ortega; Weighted inequalities for Hardy-Steklov operators; Canadian Mathematical Soc; Canadian Journal Of Mathematics; 59; 2; 12-2007; 276-295 0008-414X CONICET Digital CONICET |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
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info:eu-repo/semantics/altIdentifier/doi/10.4153/CJM-2007-011-x |
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openAccess |
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Canadian Mathematical Soc |
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Canadian Mathematical Soc |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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