A Local Estimate for the Maximal Function in Lebesgue Spaces with EXP-Type Exponents
It is proven that if 1≤p(·)<∞ in a bounded domain Ω⊂Rn and if p(·)∈EXPa(Ω) for some a>0, then given f∈Lp(·)(Ω), the Hardy-Littlewood maximal function of f, Mf, is such that p(·)log(Mf)∈EXPa/(a+1)(Ω). Because a/(a+1)<1, the thesis is slightly weaker than (Mf)λp(·)∈L1(Ω) for some λ>0. The...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/581064 |