On a Weighted Singular Integral Operator with Shifts and Slowly Oscillating Data

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• 作者：Alexei Yu. Karlovich ; Yuri I. Karlovich…
• 刊名：Complex Analysis and Operator Theory
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：10
• 期：6
• 页码：1101-1131
• 全文大小：664 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Operator Theory
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1661-8262
• 卷排序：10

文摘

Let \(\alpha ,\beta \) be orientation-preserving diffeomorphism (shifts) of \(\mathbb {R}_+=(0,\infty )\) onto itself with the only fixed points \(0\) and \(\infty \) and \(U_\alpha ,U_\beta \) be the isometric shift operators on \(L^p(\mathbb {R}_+)\) given by \(U_\alpha f=(\alpha ')^{1/p}(f\circ \alpha )\), \(U_\beta f=(\beta ')^{1/p}(f\circ \beta )\), and \(P_2^\pm =(I\pm S_2)/2\) where $$\begin{aligned} (S_2 f)(t):=\frac{1}{\pi i}\int \limits _0^\infty \left( \frac{t}{\tau }\right) ^{1/2-1/p}\frac{f(\tau )}{\tau -t}\,d\tau , \quad t\in \mathbb {R}_+, \end{aligned}$$