@article {7465,
	title = {Algebras of singular integral operators on rearrangement-invariant spaces and Nikolski ideals},
	journal = {The New York Journal of Mathematics},
	volume = {8},
	year = {2002},
	pages = {215-234},
	abstract = {<script src={\textquoteright}https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML{\textquoteright}></script><p>We construct a presymbol for the Banach algebra \(\operatorname{alg}(\Omega, S)\) generated by the Cauchy singular integral operator \(S\) and the operators of multiplication by functions in a Banach subalgebra \(\Omega\) of \(L^\infty\). This presymbol is a homomorphism \(\operatorname{alg}(\Omega,S)\to\Omega\oplus\Omega\) whose kernel coincides with the commutator ideal of \(\operatorname{alg}(\Omega,S)\). In terms of the presymbol, necessary conditions for Fredholmness of an operator in \(\operatorname{alg}(\Omega,S)\) are proved. All operators are considered on reflexive rearrangement-invariant spaces with nontrivial Boyd indices over the unit circle.</p>
},
	url = {http://www.emis.de/journals/NYJM/j/2002/8-14.html},
	author = {Karlovich, Alexei Yu.}
}
