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Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup

2010-03Journal article Open access
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dc.contributor.authorRafeiro, Humberto
dc.contributor.authorSamko, Stefan
dc.date.accessioned2018-12-07T14:53:44Z
dc.date.available2018-12-07T14:53:44Z
dc.date.issued2010-03
dc.description.abstractUnder the standard assumptions on the variable exponent p(x) (log- and decay conditions), we give a characterization of the variable exponent Bessel potential space B(alpha)[L(p(-))(R(n))] in terms of the rate of convergence of the Poisson semigroup P(t). We show that the existence of the Riesz fractional derivative D(alpha) f in the space L(p(-))(R(n)) is equivalent to the existence of the limit 1/epsilon(alpha)(I - P(epsilon))(alpha) f. In the pre-limiting case sup(x) p(x) < n/alpha we show that the Bessel potential space is characterized by the condition parallel to(I - P(epsilon))(alpha) f parallel to p((.)) <= C epsilon(alpha). (C) 2009 Elsevier Inc. All rights reserved.
dc.description.sponsorshipFundacao para a Ciencia e a Tecnologia (FCT) [SFRFi/BD/22977/2005]
dc.identifier.doi10.1016/j.jmaa.2009.11.008
dc.identifier.issn0022-247X
dc.identifier.urihttp://hdl.handle.net/10400.1/11664
dc.language.isoeng
dc.peerreviewedyes
dc.publisherAcademic Press Inc Elsevier Science
dc.subjectL-P Spaces
dc.subjectMaximal-Function
dc.subjectLebesgue Spaces
dc.subjectOperators
dc.titleCharacterization of the variable exponent Bessel potential spaces via the Poisson semigroup
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage497
oaire.citation.issue2
oaire.citation.startPage483
oaire.citation.titleJournal of Mathematical Analysis and Applications
oaire.citation.volume365
person.familyNameRafeiro
person.familyNameSamko
person.givenNameHumberto
person.givenNameStefan
person.identifier.ciencia-idA11D-7922-0F8C
person.identifier.orcid0000-0002-5304-8572
person.identifier.orcid0000-0002-8022-2863
person.identifier.ridM-3726-2013
person.identifier.scopus-author-id23390151800
person.identifier.scopus-author-id6603416048
rcaap.rightsopenAccess
rcaap.typearticle
relation.isAuthorOfPublication8d9bbd99-20b4-4a45-8d13-8f0c90ebd0e8
relation.isAuthorOfPublication7c853bfc-1d1b-4bd0-9b94-1005fafbd6a4
relation.isAuthorOfPublication.latestForDiscovery8d9bbd99-20b4-4a45-8d13-8f0c90ebd0e8

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