@article { ISI:000206111300006,
	title = {Semi-Fredholm singular integral operators with piecewise continuous coefficients on weighted variable Lebesgue spaces are Fredholm},
	journal = {Operators and Matrices},
	volume = {1},
	number = {{3}},
	year = {2007},
	pages = {427-444},
	publisher = {{ELEMENT}},
	type = {{Article}},
	address = {{R AUSTRIJE 11, 10000 ZAGREB, CROATIA}},
	abstract = {<script src={\textquoteright}https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML{\textquoteright}></script><p>Suppose \(\Gamma\) is a Carleson Jordan curve with logarithmic whirl points, \(\varrho\) is a Khvedelidze weight, \(p:\Gamma\to(1,\infty)\) is a continuous function satisfying \(|p(\tau)-p(t)|\le -\mathrm{const}/\log|\tau-t|\) for \(|\tau-t|\le 1/2\), and \(L^{p(\cdot)}(\Gamma,\varrho)\) is a weighted generalized Lebesgue space with variable exponent. We prove that all semi-Fredholm operators in the algebra of singular integral operators with \(N\times N\) matrix piecewise continuous coefficients are Fredholm on \(L_N^{p(\cdot)}(\Gamma,\varrho)\).</p>
},
	keywords = {Carleson curve, generalized Lebesgue space with variable exponent, Khvedelidze weight, singular integral operator}, {Semi-Fredholm operator},
	issn = {{1846-3886}},
	url = {http://oam.ele-math.com/01-25/Semi-Fredholm-singular-integral-operators-with-piecewise-continuous-coefficients-on-weighted-variable-Lebesgue-spaces-are-Fredholm},
	author = {Karlovich, Alexei Yu.}
}
