@article { ISI:000294097000049,
	title = {On singular integral operators with semi-almost periodic coefficients on variable Lebesgue spaces},
	journal = {Journal of Mathematical Analysis and Appliactions},
	volume = {384},
	number = {{2}},
	year = {2011},
	month = {{DEC 15}},
	pages = {706-725},
	publisher = {{ACADEMIC PRESS INC ELSEVIER SCIENCE}},
	type = {{Article}},
	address = {{525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA}},
	abstract = {<script src={\textquoteright}https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML{\textquoteright}></script><p>Let \(a\) be a semi-almost periodic matrix function with the almost periodic representatives \(a_l\) and \(a_r\) at \(-\infty\) and \(+\infty\), respectively. Suppose \(p:\mathbb{R}\to(1,\infty)\) is a slowly oscillating exponent such that the Cauchy singular integral operator \(S\) is bounded on the variable Lebesgue space \(L^{p(\cdot)}(\mathbb{R})\). We prove that if the operator \(aP+Q\) with \(P=(I+S)/2\) and \(Q=(I-S)/2\) is Fredholm on the variable Lebesgue space \(L_N^{p(\cdot)}(\mathbb{R})\), then the operators \(a_lP+Q\) and \(a_rP+Q\) are invertible on standard Lebesgue spaces \(L_N^{q_l}(\mathbb{R})\) and \(L_N^{q_r}(\mathbb{R})\) with some exponents \(q_l\) and \(q_r\) lying in the segments between the lower and the upper limits of \(p\) at \(-\infty\) and \(+\infty\), respectively. </p>
},
	keywords = {Fredholmness, Invertibility}, Semi-almost periodic function, Singular integral operator, slowly oscillating function, Variable Lebesgue space, {Almost-periodic function},
	issn = {{0022-247X}},
	doi = {{10.1016/j.jmaa.2011.06.066}},
	url = {http://www.sciencedirect.com/science/article/pii/S0022247X11006147},
	author = {Karlovich, Alexei Yu and Spitkovsky, Ilya M.}
}
