Maximal Operator in Variable Exponent Lebesgue Spaces on Unbounded Quasimetric Measure Spaces
Keyword(s):
We study the Hardy-Littlewood maximal operator $M$ on $L^{p({\cdot})}(X)$ when $X$ is an unbounded (quasi)metric measure space, and $p$ may be unbounded. We consider both the doubling and general measure case, and use two versions of the $\log$-Hölder condition. As a special case we obtain the criterion for a boundedness of $M$ on $L^{p({\cdot})}({\mathsf{R}^n},\mu)$ for arbitrary, possibly non-doubling, Radon measures.
2005 ◽
Vol 30
(1)
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pp. 87
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1963 ◽
Vol 6
(2)
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pp. 211-229
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Keyword(s):
2007 ◽
Vol 280
(1-2)
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pp. 74-82
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1998 ◽
Vol 128
(2)
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pp. 403-424
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2014 ◽
Vol 8
(2)
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pp. 229-244
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Keyword(s):