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The maximal operator on weighted variable Lebesgue spaces

✍ Scribed by David Cruz-Uribe; Lars Diening; Peter Hästö

Book ID
111493516
Publisher
SP Versita
Year
2011
Tongue
English
Weight
237 KB
Volume
14
Category
Article
ISSN
1311-0454

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## Abstract This article contains results about the boundedness of the Hardy–Littlewood maximal operator in variable exponent Lebesgue spaces. We study the situation where the exponent approaches one in some parts of the domain. We show that the boundedness depends on how fast the exponent approach

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## 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