Fredholmness and index of simplest weighted singular integral operators with two slowly oscillating shifts

Detalhes bibliográficos
Autor(a) principal: Karlovych, Oleksiy
Data de Publicação: 2015
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/23469
Resumo: This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project PEst-OE/MAT/UIO297/2014 (Centro de Matemdtica e Aplicacoes). The authors would like to thank the anonymous referee for useful remarks and for informing about the work [5].
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spelling Fredholmness and index of simplest weighted singular integral operators with two slowly oscillating shiftsweighted singular integraloperatorslowly oscillating shiftindexMellin pseudodierential operatorFredholmnessFredholmnessIndexMellin pseudodifferential operatorSlowly oscillating shiftWeighted singular integral operatorThis work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project PEst-OE/MAT/UIO297/2014 (Centro de Matemdtica e Aplicacoes). The authors would like to thank the anonymous referee for useful remarks and for informing about the work [5].Let α and β be orientation-preserving diffeomorphisms (shifts) of R+ = (0, ∞) onto itself with the only fixed points 0 and ∞, where the derivatives α' and β' may have discontinuities of slowly oscillating type at 0 and ∞ For p ∈ (1 ∞), we consider the weighted shift operators Uα and Uβ given on the Lebesgue space Lp(R+) by Uαf = (α')1/p(f o α) and Uβf = (β')1/p(f o β). For i, j ∈ Z we study the simplest weighted singular integral operators with two shifts Aij = Uα iP+ γ + Uβ jP- γ on Lp(R+), where P± γ = (I ± Sγ)/2 are operators associated to theweighted Cauchy singular integral operator with γ ∈ C satisfying 0 < 1/p + Rγ < 1. We prove that the operator Aij is a Fredholm operator on Lp(R+) and has zero index if where wij (t) = log[αi (β-j (t))/t] and αi, β-j are iterations of α, β. This statement extends an earlier result obtained by the author, Yuri Karlovich, and Amarino Lebre for γ = 0.DM - Departamento de MatemáticaCMA - Centro de Matemática e AplicaçõesRUNKarlovych, Oleksiy2017-09-20T22:00:19Z20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10362/23469eng1735-8787PURE: 139092https://doi.org/10.15352/bjma/09-3-3info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-03-11T04:11:45Zoai:run.unl.pt:10362/23469Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:27:48.854371Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Fredholmness and index of simplest weighted singular integral operators with two slowly oscillating shifts
title Fredholmness and index of simplest weighted singular integral operators with two slowly oscillating shifts
spellingShingle Fredholmness and index of simplest weighted singular integral operators with two slowly oscillating shifts
Karlovych, Oleksiy
weighted singular integraloperator
slowly oscillating shift
index
Mellin pseudodierential operator
Fredholmness
Fredholmness
Index
Mellin pseudodifferential operator
Slowly oscillating shift
Weighted singular integral operator
title_short Fredholmness and index of simplest weighted singular integral operators with two slowly oscillating shifts
title_full Fredholmness and index of simplest weighted singular integral operators with two slowly oscillating shifts
title_fullStr Fredholmness and index of simplest weighted singular integral operators with two slowly oscillating shifts
title_full_unstemmed Fredholmness and index of simplest weighted singular integral operators with two slowly oscillating shifts
title_sort Fredholmness and index of simplest weighted singular integral operators with two slowly oscillating shifts
author Karlovych, Oleksiy
author_facet Karlovych, Oleksiy
author_role author
dc.contributor.none.fl_str_mv DM - Departamento de Matemática
CMA - Centro de Matemática e Aplicações
RUN
dc.contributor.author.fl_str_mv Karlovych, Oleksiy
dc.subject.por.fl_str_mv weighted singular integraloperator
slowly oscillating shift
index
Mellin pseudodierential operator
Fredholmness
Fredholmness
Index
Mellin pseudodifferential operator
Slowly oscillating shift
Weighted singular integral operator
topic weighted singular integraloperator
slowly oscillating shift
index
Mellin pseudodierential operator
Fredholmness
Fredholmness
Index
Mellin pseudodifferential operator
Slowly oscillating shift
Weighted singular integral operator
description This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project PEst-OE/MAT/UIO297/2014 (Centro de Matemdtica e Aplicacoes). The authors would like to thank the anonymous referee for useful remarks and for informing about the work [5].
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-01-01T00:00:00Z
2017-09-20T22:00:19Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/23469
url http://hdl.handle.net/10362/23469
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1735-8787
PURE: 139092
https://doi.org/10.15352/bjma/09-3-3
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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