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Zbl 0946.45006
Samko, N.
Singular integral operators in weighted spaces with generalized Hölder condition.
(English)
[J] Proc. A. Razmadze Math. Inst. 120, 107-134 (1999). ISSN 1512-0007

The author considers the singular integral operator $N=aI+bS$ with piecewise continuous coefficients in the generalized weighted Hölder spaces $H^\omega_0(\Gamma,\rho)$ , where $\Gamma$ is a generalized Lyapunov curve and $\rho(t)=\prod_{k=0}^n r_k(|t-t_k|)$ with $r_k(t)$ from some class $V_\alpha$. A boundedness condition in this space for the singular operator $S$ in terms of the characteristic $\omega(t)$ is described. Fredholmness conditions for the operator $N$ and a formula for calculating its index are given in terms of the so called index numbers of the characteristic $\omega(t)$ as well as some connections between these characteristics and some characteristics of the functions $r_k(t)$.
[N.K.Karapetyants (Rostov-na-Donu)]
MSC 2000:
*45P05 Integral operators
45E05 Integral equations with kernels of Cauchy type
47A53 (Semi-)Fredholm operators; index theories

Keywords: generalized Hölder spaces; singular integral operators; Boyd indices; Fredholm operator; index

Cited in: Zbl 1036.47035

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