A sharpness result for powers of Besov functions
A recent result of Kateb asserts that f∈Bp,qs(ℝn) implies |f|μ∈Bp,qs(ℝn) as soon as the following three conditions hold: (1) 0≺s≺μ+(1/p), (2) f is bounded, (3) μ≻1. By means of counterexamples, we prove that those conditions are optimal.
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2004/823103 |
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| _version_ | 1850168955493154816 |
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| author | Gérard Bourdaud |
| author_facet | Gérard Bourdaud |
| author_sort | Gérard Bourdaud |
| collection | DOAJ |
| description | A recent result of Kateb asserts that f∈Bp,qs(ℝn) implies |f|μ∈Bp,qs(ℝn) as soon as the following three conditions hold: (1) 0≺s≺μ+(1/p), (2) f is bounded, (3) μ≻1. By means of counterexamples, we prove that those conditions are optimal. |
| format | Article |
| id | doaj-art-9fd30afcf0844910a2a552a96a5d91dd |
| institution | OA Journals |
| issn | 0972-6802 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-9fd30afcf0844910a2a552a96a5d91dd2025-08-20T02:20:51ZengWileyJournal of Function Spaces and Applications0972-68022004-01-012326727710.1155/2004/823103A sharpness result for powers of Besov functionsGérard Bourdaud0Institut de Mathématiques de Jussieu, Équipe d'Analyse Fonctionnelle, Case 186, 4 place Jussieu, 75252 Paris Cedex 05, FranceA recent result of Kateb asserts that f∈Bp,qs(ℝn) implies |f|μ∈Bp,qs(ℝn) as soon as the following three conditions hold: (1) 0≺s≺μ+(1/p), (2) f is bounded, (3) μ≻1. By means of counterexamples, we prove that those conditions are optimal.http://dx.doi.org/10.1155/2004/823103 |
| spellingShingle | Gérard Bourdaud A sharpness result for powers of Besov functions Journal of Function Spaces and Applications |
| title | A sharpness result for powers of Besov functions |
| title_full | A sharpness result for powers of Besov functions |
| title_fullStr | A sharpness result for powers of Besov functions |
| title_full_unstemmed | A sharpness result for powers of Besov functions |
| title_short | A sharpness result for powers of Besov functions |
| title_sort | sharpness result for powers of besov functions |
| url | http://dx.doi.org/10.1155/2004/823103 |
| work_keys_str_mv | AT gerardbourdaud asharpnessresultforpowersofbesovfunctions AT gerardbourdaud sharpnessresultforpowersofbesovfunctions |