A carregar...
Publicação
Fredholmness and index of simplest weighted singular integral operators with two slowly oscillating shifts
| Nome: | Descrição: | Tamanho: | Formato: | |
|---|---|---|---|---|
| 461.23 KB | Adobe PDF |
Autores
Orientador(es)
Resumo(s)
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.
Descrição
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].
Palavras-chave
weighted singular integraloperator slowly oscillating shift index Mellin pseudodierential operator Fredholmness Fredholmness Index Mellin pseudodifferential operator Slowly oscillating shift Weighted singular integral operator
Contexto Educativo
Citação
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