The maximal operator on weighted variable Lebesgue spaces

We study the boundedness of the maximal operator on the weighted variable exponent Lebesgue spaces L ω p (·) (Ω). For a given log-Hölder continuous exponent p with 1 < inf p ⩽ sup p < ∞ we present a necessary and sufficient condition on the weight ω for the boundedness of M . This condition is...

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Bibliographic Details
Published in:Fractional calculus & applied analysis 2011-09, Vol.14 (3), p.361-374
Main Authors: Cruz-Uribe, David, Diening, Lars, Hästö, Peter
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Analysis
Functional Analysis
Integral Transforms
Mathematics
Mathematics and Statistics
maximal operator
Muckenhoupt weights
Operational Calculus
Primary 42B25
Research Paper
Secondary 42B35
variable exponent Lebesgue spaces
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Summary:We study the boundedness of the maximal operator on the weighted variable exponent Lebesgue spaces L ω p (·) (Ω). For a given log-Hölder continuous exponent p with 1 < inf p ⩽ sup p < ∞ we present a necessary and sufficient condition on the weight ω for the boundedness of M . This condition is a generalization of the classical Muckenhoupt condition.
ISSN:1311-0454
1314-2224
DOI:10.2478/s13540-011-0023-7