@article { ISI:000292886900001,
	title = {Sufficient conditions for Fredholmness of singular integral operators with shifts and slowly oscillating data},
	journal = {Integral Equations and Operator Theory},
	volume = {70},
	number = {{4}},
	year = {2011},
	month = {{AUG}},
	pages = {451-483},
	publisher = {{BIRKHAUSER VERLAG AG}},
	type = {{Article}},
	address = {{VIADUKSTRASSE 40-44, PO BOX 133, CH-4010 BASEL, SWITZERLAND}},
	abstract = {<script src={\textquoteright}https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML{\textquoteright}></script><p>Suppose \(\alpha\) is an orientation preserving diffeomorphism (shift) of \(\mathbb{R}_+=(0,\infty)\)  onto itself with the only fixed points \(0\) and \(\infty\). We establish sufficient conditions for the Fredholmness of the singular integral operator with shift \[ (aI-bW_\alpha)P_++(cI-dW_\alpha)P_- \] acting on \(L^p(\mathbb{R}_+)\) with \( 1 \&lt; p \&lt; \infty \), where \(P_\pm=(I\pm S)/2\), \(S\) is the Cauchy singular integral operator, and \(W_\alpha f=f\circ\alpha\) is the shift operator, under the assumptions that the coefficients \(a,b,c,d\) and the derivative \(\alpha{\textquoteright}\) of the shift are bounded and continuous on \(\mathbb{R}_+\) and may admit discontinuities of slowly oscillating type at \(0\) and \(\infty\). </p>
},
	keywords = {Cauchy singular integral operator, Fredholmness}, Mellin pseudodifferential operator, slowly oscillating function, {Orientation-preserving non-Carleman shift},
	issn = {{0378-620X}},
	doi = {{10.1007/s00020-010-1861-0}},
	url = {http://www.springerlink.com/content/cg76170280775q2t/},
	author = {Karlovich, Alexei Yu and Karlovich, Yuri I. and Lebre, Amarino B.}
}
