@article { ISI:000274138500006,
	title = {Maximal operators on variable Lebesgue spaces with weights related to oscillations of Carleson curves},
	journal = {Mathematische Nachrichten},
	volume = {283},
	number = {{1}},
	year = {2010},
	month = {{JAN}},
	pages = {85-93},
	publisher = {{WILEY-V C H VERLAG GMBH}},
	type = {{Article}},
	address = {{PO BOX 10 11 61, D-69451 WEINHEIM, GERMANY}},
	abstract = {<script src={\textquoteright}https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML{\textquoteright}></script><p>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.</p>
},
	keywords = {Carleson curve, Dini-Lipschitz condition, indices of submultiplicative function, oscillating weight, spirality indices}, weighted variable Lebesgue space, {Maximal operator},
	issn = {{0025-584X}},
	doi = {{10.1002/mana.200810295}},
	url = {http://onlinelibrary.wiley.com/doi/10.1002/mana.200810295/abstract},
	author = {Karlovich, Alexei Yu.}
}
