Abstract
In a previous paper we found conditions for a singular integral operator with piecewise continuous coefficients to be Fredholm in a weighted generalized Hölder space H ω0 (Γ, ρ) together with a formula for the index. The conditions were given in terms of Boyd-type indices of the space H ω0 (Γ, ρ). In this paper we prove that those conditions are also necessary for a singular integral operator to be Fredholm.
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Samko, N. (2003). Criterion for the Fredholmness of Singular Operators with Piecewise Continuous Coefficients in Generalized Hölder Spaces with Weight. In: Böttcher, A., Kaashoek, M.A., Lebre, A.B., dos Santos, A.F., Speck, FO. (eds) Singular Integral Operators, Factorization and Applications. Operator Theory: Advances and Applications, vol 142. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8007-7_18
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DOI: https://doi.org/10.1007/978-3-0348-8007-7_18
Publisher Name: Birkhäuser, Basel
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