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}
}
  • A. Karlovich
  • Published 2 May 2014
  • Mathematics
  • arXiv: Functional Analysis
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… 
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