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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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/581064 |
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| author | Alberto Fiorenza |
| author_facet | Alberto Fiorenza |
| author_sort | Alberto Fiorenza |
| collection | DOAJ |
| description | 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 assumption that p(·)∈EXPa(Ω) for some a>0 is proven to be optimal in the framework of the Orlicz spaces to obtain p(·)log(Mf) in the same class of spaces. |
| format | Article |
| id | doaj-art-465af6a923a140978969b6a06c57a07b |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-465af6a923a140978969b6a06c57a07b2025-02-03T06:11:00ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/581064581064A Local Estimate for the Maximal Function in Lebesgue Spaces with EXP-Type ExponentsAlberto Fiorenza0Dipartimento di Architettura, Università di Napoli, Via Monteoliveto 3, 80134 Napoli, ItalyIt 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 assumption that p(·)∈EXPa(Ω) for some a>0 is proven to be optimal in the framework of the Orlicz spaces to obtain p(·)log(Mf) in the same class of spaces.http://dx.doi.org/10.1155/2015/581064 |
| spellingShingle | Alberto Fiorenza A Local Estimate for the Maximal Function in Lebesgue Spaces with EXP-Type Exponents Journal of Function Spaces |
| title | A Local Estimate for the Maximal Function in Lebesgue Spaces with EXP-Type Exponents |
| title_full | A Local Estimate for the Maximal Function in Lebesgue Spaces with EXP-Type Exponents |
| title_fullStr | A Local Estimate for the Maximal Function in Lebesgue Spaces with EXP-Type Exponents |
| title_full_unstemmed | A Local Estimate for the Maximal Function in Lebesgue Spaces with EXP-Type Exponents |
| title_short | A Local Estimate for the Maximal Function in Lebesgue Spaces with EXP-Type Exponents |
| title_sort | local estimate for the maximal function in lebesgue spaces with exp type exponents |
| url | http://dx.doi.org/10.1155/2015/581064 |
| work_keys_str_mv | AT albertofiorenza alocalestimateforthemaximalfunctioninlebesguespaceswithexptypeexponents AT albertofiorenza localestimateforthemaximalfunctioninlebesguespaceswithexptypeexponents |