Hölder norm estimate for the fractal Hilbert transform in Douglis analysis

Douglis analysis is an alternative approach to complex methods for the investigation of linear and uniformly elliptic systems of 2n equations for 2n desired real-valued functions. The function theory associated with the Douglis operator in R2 (identifying R2 with C in the usual way) plays a very imp...

ver descrição completa

Detalhes bibliográficos
Autores: Peña Perez, Yudier, Arciga Alejandre, Martin Patricio, Bory Reyes, Juan
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:México
Recursos:Universidad Autónoma de Guerrero
Repositorio:Repositorio Institucional de Ciencia Abierta de la Universidad Autónoma de Guerrero
Idioma:inglés
OAI Identifier:oai:ri.uagro.mx:uagro/941
Acesso em linha:http://ri.uagro.mx/handle/uagro/941
Access Level:acceso abierto
Palavra-chave:Tesauro digital complutense TDC /funciones
Tesauro digital complutense TDC /dimensiones
Tesauro digital complutense TDC /fractales
Tesauro digital complutense TDC /Descomposición
CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA::MATEMÁTICAS::ANÁLISIS Y ANÁLISIS FUNCIONAL::OTRAS
id MX_634ecdc91f17c28c4398fc68eab2d896
oai_identifier_str oai:ri.uagro.mx:uagro/941
network_acronym_str MX
network_name_str México
repository_id_str
spelling Hölder norm estimate for the fractal Hilbert transform in Douglis analysisPeña Perez, YudierArciga Alejandre, Martin PatricioBory Reyes, JuanTesauro digital complutense TDC /funcionesTesauro digital complutense TDC /dimensionesTesauro digital complutense TDC /fractalesTesauro digital complutense TDC /DescomposiciónCIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA::MATEMÁTICAS::ANÁLISIS Y ANÁLISIS FUNCIONAL::OTRASDouglis analysis is an alternative approach to complex methods for the investigation of linear and uniformly elliptic systems of 2n equations for 2n desired real-valued functions. The function theory associated with the Douglis operator in R2 (identifying R2 with C in the usual way) plays a very important role in problems in pure mathematics, mathematical physics, and engineering, such as plane elasticity theory and hydromechanics. The well-known Douglis system, that is, an elliptic system of first order in two inde- pendent variables, can be represented by a single "hypercomplex" equation. Solutions of such equation (null solutions of the Douglis system) are termed hyperanalytic functions. In [1] Douglis presented a complete study of the hyperanalytic function theory. For greater details the reader is directed to [2] and to [3] for a thorough treatment of this theory. In more recent times hyperanalytic function theory has been developed for solving problems of mathematical physics such as plate and shell problems. In [4, 5] the authors provided conditions for the solvability of the Riemann boundary value problem for hy- peranalytic functions on classes of fractal closed curves. Hence, this can be regarded of as a good motivation for finding conditions on the boundary, which give boundedness of certain singular integral operators, such as the Hilbert transform when the boundary is permitted to be fractal. To this end, in [6] the authors gave an estimate for the upper bound of the Hölder norm a fractal version of the Hilbert transform for domains with d-summable boundary; a geometric notion introduced in [7], which is essential for inte- gration of a form over a fractal boundary.Springer2019-10-01T16:24:10Z2019-10-01T16:24:10Z2017-03-21Artículoinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlepdfBorn digitalapplication/pdfhttp://ri.uagro.mx/handle/uagro/9411625080010.1186/s13660-017-1488-7reponame:Repositorio Institucional de Ciencia Abierta de la Universidad Autónoma de Guerreroinstname:Universidad Autónoma de Guerreroinstacron:UAGROenghttp://creativecommons.org/licenses/by-nc-nd/4.0openAccessinfo:eu-repo/semantics/openAccessoai:ri.uagro.mx:uagro/9412024-08-28T00:01:02Z
dc.title.none.fl_str_mv Hölder norm estimate for the fractal Hilbert transform in Douglis analysis
title Hölder norm estimate for the fractal Hilbert transform in Douglis analysis
spellingShingle Hölder norm estimate for the fractal Hilbert transform in Douglis analysis
Peña Perez, Yudier
Tesauro digital complutense TDC /funciones
Tesauro digital complutense TDC /dimensiones
Tesauro digital complutense TDC /fractales
Tesauro digital complutense TDC /Descomposición
CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA::MATEMÁTICAS::ANÁLISIS Y ANÁLISIS FUNCIONAL::OTRAS
title_short Hölder norm estimate for the fractal Hilbert transform in Douglis analysis
title_full Hölder norm estimate for the fractal Hilbert transform in Douglis analysis
title_fullStr Hölder norm estimate for the fractal Hilbert transform in Douglis analysis
title_full_unstemmed Hölder norm estimate for the fractal Hilbert transform in Douglis analysis
title_sort Hölder norm estimate for the fractal Hilbert transform in Douglis analysis
dc.creator.none.fl_str_mv Peña Perez, Yudier
Arciga Alejandre, Martin Patricio
Bory Reyes, Juan
author Peña Perez, Yudier
author_facet Peña Perez, Yudier
Arciga Alejandre, Martin Patricio
Bory Reyes, Juan
author_role author
author2 Arciga Alejandre, Martin Patricio
Bory Reyes, Juan
author2_role author
author
dc.subject.none.fl_str_mv Tesauro digital complutense TDC /funciones
Tesauro digital complutense TDC /dimensiones
Tesauro digital complutense TDC /fractales
Tesauro digital complutense TDC /Descomposición
CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA::MATEMÁTICAS::ANÁLISIS Y ANÁLISIS FUNCIONAL::OTRAS
topic Tesauro digital complutense TDC /funciones
Tesauro digital complutense TDC /dimensiones
Tesauro digital complutense TDC /fractales
Tesauro digital complutense TDC /Descomposición
CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA::MATEMÁTICAS::ANÁLISIS Y ANÁLISIS FUNCIONAL::OTRAS
description Douglis analysis is an alternative approach to complex methods for the investigation of linear and uniformly elliptic systems of 2n equations for 2n desired real-valued functions. The function theory associated with the Douglis operator in R2 (identifying R2 with C in the usual way) plays a very important role in problems in pure mathematics, mathematical physics, and engineering, such as plane elasticity theory and hydromechanics. The well-known Douglis system, that is, an elliptic system of first order in two inde- pendent variables, can be represented by a single "hypercomplex" equation. Solutions of such equation (null solutions of the Douglis system) are termed hyperanalytic functions. In [1] Douglis presented a complete study of the hyperanalytic function theory. For greater details the reader is directed to [2] and to [3] for a thorough treatment of this theory. In more recent times hyperanalytic function theory has been developed for solving problems of mathematical physics such as plate and shell problems. In [4, 5] the authors provided conditions for the solvability of the Riemann boundary value problem for hy- peranalytic functions on classes of fractal closed curves. Hence, this can be regarded of as a good motivation for finding conditions on the boundary, which give boundedness of certain singular integral operators, such as the Hilbert transform when the boundary is permitted to be fractal. To this end, in [6] the authors gave an estimate for the upper bound of the Hölder norm a fractal version of the Hilbert transform for domains with d-summable boundary; a geometric notion introduced in [7], which is essential for inte- gration of a form over a fractal boundary.
publishDate 2017
dc.date.none.fl_str_mv 2017-03-21
2019-10-01T16:24:10Z
2019-10-01T16:24:10Z
dc.type.none.fl_str_mv Artículo
info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://ri.uagro.mx/handle/uagro/941
16250800
10.1186/s13660-017-1488-7
url http://ri.uagro.mx/handle/uagro/941
identifier_str_mv 16250800
10.1186/s13660-017-1488-7
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0
openAccess
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0
openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv pdf
Born digital
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositorio Institucional de Ciencia Abierta de la Universidad Autónoma de Guerrero
instname:Universidad Autónoma de Guerrero
instacron:UAGRO
instname_str Universidad Autónoma de Guerrero
instacron_str UAGRO
institution UAGRO
reponame_str Repositorio Institucional de Ciencia Abierta de la Universidad Autónoma de Guerrero
collection Repositorio Institucional de Ciencia Abierta de la Universidad Autónoma de Guerrero
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1858175493151391744
score 15,811543

Registos relacionados