✦ LIBER ✦
Maximal operators on variable Lebesgue spaces with weights related to oscillations of Carleson curves
✍ Scribed by Alexei Yu. Karlovich
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 142 KB
- Volume
- 283
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
We prove sufficient conditions for the boundedness of the maximal operator on variable Lebesgue spaces with weights φ~t,γ~ (τ) = |(τ – t)^γ^ |, where γ is a complex number, over arbitrary Carleson curves. If the curve has different spirality indices at the point t and γ is not real, then φ~t,γ~ is an oscillating weight lying beyond the class of radial oscillating weights considered recently by V. Kokilashvili, N. Samko, and S. Samko (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)