<?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></authors></contributors><titles><title><style face="normal" font="default" size="100%">Maximal operators on variable Lebesgue spaces with weights related to oscillations of Carleson curves</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematische Nachrichten</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Carleson curve</style></keyword><keyword><style  face="normal" font="default" size="100%">Dini-Lipschitz condition</style></keyword><keyword><style  face="normal" font="default" size="100%">indices of submultiplicative function</style></keyword><keyword><style  face="normal" font="default" size="100%">oscillating weight</style></keyword><keyword><style  face="normal" font="default" size="100%">spirality indices}</style></keyword><keyword><style  face="normal" font="default" size="100%">weighted variable Lebesgue space</style></keyword><keyword><style  face="normal" font="default" size="100%">{Maximal operator</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">{JAN}</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://onlinelibrary.wiley.com/doi/10.1002/mana.200810295/abstract</style></url></web-urls></urls><number><style face="normal" font="default" size="100%">{1}</style></number><publisher><style face="normal" font="default" size="100%">{WILEY-V C H VERLAG GMBH}</style></publisher><pub-location><style face="normal" font="default" size="100%">{PO BOX 10 11 61, D-69451 WEINHEIM, GERMANY}</style></pub-location><volume><style face="normal" font="default" size="100%">283</style></volume><pages><style face="normal" font="default" size="100%">85-93</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;We prove sufficient conditions for the boundedness of the maximal operator on variable Lebesgue spaces with weights \(\varphi_{t,\gamma}(\tau)=|(\tau-t)^\gamma|\), where \(\gamma\) is a complex number, over arbitrary Carleson curves. If the curve has different spirality indices at the point $t$ and \(\gamma\) is not real, then \(\varphi_{t,\gamma}\) is an oscillating weight lying beyond the class of radial oscillating weights considered recently by V. Kokilashvili, N. Samko, and S. Samko.&lt;/p&gt;
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