Publicação
Fredholmness and index of simplest weighted singular integral operators with two slowly oscillating shifts
| dc.contributor.author | Karlovych, Oleksiy | |
| dc.contributor.institution | DM - Departamento de Matemática | |
| dc.contributor.institution | CMA - Centro de Matemática e Aplicações | |
| dc.date.accessioned | 2017-09-20T22:00:19Z | |
| dc.date.available | 2017-09-20T22:00:19Z | |
| dc.date.issued | 2015 | |
| dc.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]. | |
| dc.description.abstract | 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. | en |
| dc.description.version | proof | |
| dc.description.version | published | |
| dc.identifier.citation | Karlovych, O. (2015). Fredholmness and index of simplest weighted singular integral operators with two slowly oscillating shifts. Banach Journal Of Mathematical Analysis, 9(3), 24-42. https://doi.org/10.15352/bjma/09-3-3 | |
| dc.identifier.doi | https://doi.org/10.15352/bjma/09-3-3 | |
| dc.identifier.issn | 1735-8787 | |
| dc.identifier.other | PURE: 139092 | |
| dc.identifier.other | PURE UUID: 0a8cb16c-6542-47dc-b3e9-2e18581d6c9a | |
| dc.identifier.other | researchoutputwizard: 46397 | |
| dc.identifier.other | WOS: 000352239000003 | |
| dc.identifier.other | Scopus: 84919674826 | |
| dc.identifier.uri | http://hdl.handle.net/10362/23469 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.subject | weighted singular integraloperator | |
| dc.subject | slowly oscillating shift | |
| dc.subject | index | |
| dc.subject | Mellin pseudodierential operator | |
| dc.subject | Fredholmness | |
| dc.subject | Fredholmness | |
| dc.subject | Index | |
| dc.subject | Mellin pseudodifferential operator | |
| dc.subject | Slowly oscillating shift | |
| dc.subject | Weighted singular integral operator | |
| dc.title | Fredholmness and index of simplest weighted singular integral operators with two slowly oscillating shifts | |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 42 | |
| oaire.citation.issue | 3 | |
| oaire.citation.startPage | 24 | |
| oaire.citation.title | Banach Journal Of Mathematical Analysis | |
| oaire.citation.volume | 9 | |
| rcaap.rights | openAccess | |
| rcaap.type | article |
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