Characterization of generalized Orlicz spaces

Handle URI:
http://hdl.handle.net/10754/626470
Title:
Characterization of generalized Orlicz spaces
Authors:
Ferreira, Rita ( 0000-0002-7169-9141 ) ; Hästö, Peter; Ribeiro, Ana Margarida
Abstract:
The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Because the difference quotient is based on shifting the function, it cannot be used in generalized Orlicz spaces. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the generalized Orlicz-Sobolev space. Our results are new even in Orlicz spaces and variable exponent spaces.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
arXiv
Issue Date:
14-Dec-2016
ARXIV:
arXiv:1612.04566
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1612.04566v1; http://arxiv.org/pdf/1612.04566v1
Appears in Collections:
Other/General Submission; Other/General Submission; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorFerreira, Ritaen
dc.contributor.authorHästö, Peteren
dc.contributor.authorRibeiro, Ana Margaridaen
dc.date.accessioned2017-12-28T07:32:11Z-
dc.date.available2017-12-28T07:32:11Z-
dc.date.issued2016-12-14en
dc.identifier.urihttp://hdl.handle.net/10754/626470-
dc.description.abstractThe norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Because the difference quotient is based on shifting the function, it cannot be used in generalized Orlicz spaces. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the generalized Orlicz-Sobolev space. Our results are new even in Orlicz spaces and variable exponent spaces.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1612.04566v1en
dc.relation.urlhttp://arxiv.org/pdf/1612.04566v1en
dc.rightsArchived with thanks to arXiven
dc.titleCharacterization of generalized Orlicz spacesen
dc.typePreprinten
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.eprint.versionPre-printen
dc.contributor.institutionDepartment of Mathematics and Statistics, University of Turku, Finlanden
dc.contributor.institutionDepartment of Mathematical Sciences, P.O. Box 3000, FI-90014 University of Oulu, Finlanden
dc.contributor.institutionCentro de Matematica e Aplicacoes (CMA) and Departamento de Matematica, Faculdade de Ciencias e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugalen
dc.identifier.arxividarXiv:1612.04566en
kaust.authorFerreira, Ritaen
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