# Fredholmness and Index of Simplest Weighted Singular Integral Operators with Two Slowly Oscillating Shifts

@article{Karlovich2014FredholmnessAI, title={Fredholmness and Index of Simplest Weighted Singular Integral Operators with Two Slowly Oscillating Shifts}, author={Alexei Yu. Karlovich}, journal={arXiv: Functional Analysis}, year={2014} }

Let $\alpha$ and $\beta$ be orientation-preserving diffeomorphisms (shifts) of $\mathbb{R}_+=(0,\infty)$ onto itself with the only fixed points $0$ and $\infty$, where the derivatives $\alpha'$ and $\beta'$ may have discontinuities of slowly oscillating type at $0$ and $\infty$. For $p\in(1,\infty)$, we consider the weighted shift operators $U_\alpha$ and $U_\beta$ given on the Lebesgue space $L^p(\mathbb{R}_+)$ by $U_\alpha f=(\alpha')^{1/p}(f\circ\alpha)$ and $U_\beta f= (\beta')^{1/p}(f\circ…

## 6 Citations

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We compute the generalized Cauchy index of some semi-almost periodic functions, which are important in the study of the Fredholm index of singular integral operators with shifts and slowly…

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