<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Karlovich, Alexei Yu</style></author><author><style face="normal" font="default" size="100%">Spitkovsky, Ilya M.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On singular integral operators with semi-almost periodic coefficients on variable Lebesgue spaces</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Mathematical Analysis and Appliactions</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Fredholmness</style></keyword><keyword><style  face="normal" font="default" size="100%">Invertibility}</style></keyword><keyword><style  face="normal" font="default" size="100%">Semi-almost periodic function</style></keyword><keyword><style  face="normal" font="default" size="100%">Singular integral operator</style></keyword><keyword><style  face="normal" font="default" size="100%">slowly oscillating function</style></keyword><keyword><style  face="normal" font="default" size="100%">Variable Lebesgue space</style></keyword><keyword><style  face="normal" font="default" size="100%">{Almost-periodic function</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">{DEC 15}</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.sciencedirect.com/science/article/pii/S0022247X11006147</style></url></web-urls></urls><number><style face="normal" font="default" size="100%">{2}</style></number><publisher><style face="normal" font="default" size="100%">{ACADEMIC PRESS INC ELSEVIER SCIENCE}</style></publisher><pub-location><style face="normal" font="default" size="100%">{525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA}</style></pub-location><volume><style face="normal" font="default" size="100%">384</style></volume><pages><style face="normal" font="default" size="100%">706-725</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;script src='https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML'&gt;&lt;/script&gt;&lt;p&gt;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. &lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><work-type><style face="normal" font="default" size="100%">{Article}</style></work-type></record></records></xml>