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Karlovich","submitted_at":"2014-05-02T10:05:06Z","abstract_excerpt":"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 $U_\\beta f= (\\beta')^{1/p}(f\\circ\\beta)$. 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