Explicit Bounds and Sharp Results for the Composition Operators Preserving the Exponential Class
Let f:Ω⊂Rn→Rn be a quasiconformal mapping whose Jacobian is denoted by Jf and let EXP(Ω) be the space of exponentially integrable functions on Ω. We give an explicit bound for the norm of the composition operator Tf: u∈EXP(Ω)↦u∘f-1∈EXP(f(Ω)) and, as a related question, we study the behaviour of the...
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/3769813 |
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| author | Fernando Farroni Raffaella Giova |
| author_facet | Fernando Farroni Raffaella Giova |
| author_sort | Fernando Farroni |
| collection | DOAJ |
| description | Let f:Ω⊂Rn→Rn be a quasiconformal mapping whose Jacobian is denoted by Jf and let EXP(Ω) be the space of exponentially integrable functions on Ω. We give an explicit bound for the norm of the composition operator Tf: u∈EXP(Ω)↦u∘f-1∈EXP(f(Ω)) and, as a related question, we study the behaviour of the norm of logJf in the exponential class. The A∞ property of Jf is the counterpart in higher dimensions of the area distortion formula due to Astala in the plane and it is the key tool to prove the sharpness of our results. |
| format | Article |
| id | doaj-art-2ea22790731b42da844ce1ede5b1abcb |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-2ea22790731b42da844ce1ede5b1abcb2025-02-03T05:54:07ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/37698133769813Explicit Bounds and Sharp Results for the Composition Operators Preserving the Exponential ClassFernando Farroni0Raffaella Giova1Università Telematica PEGASO, Piazza Trieste e Trento 48, 80132 Napoli, ItalyDipartimento di Studi Economici e Giuridici, Università degli Studi di Napoli “Parthenope”, Palazzo Pacanowsky, Via Generale Parisi 13, 80132 Napoli, ItalyLet f:Ω⊂Rn→Rn be a quasiconformal mapping whose Jacobian is denoted by Jf and let EXP(Ω) be the space of exponentially integrable functions on Ω. We give an explicit bound for the norm of the composition operator Tf: u∈EXP(Ω)↦u∘f-1∈EXP(f(Ω)) and, as a related question, we study the behaviour of the norm of logJf in the exponential class. The A∞ property of Jf is the counterpart in higher dimensions of the area distortion formula due to Astala in the plane and it is the key tool to prove the sharpness of our results.http://dx.doi.org/10.1155/2016/3769813 |
| spellingShingle | Fernando Farroni Raffaella Giova Explicit Bounds and Sharp Results for the Composition Operators Preserving the Exponential Class Journal of Function Spaces |
| title | Explicit Bounds and Sharp Results for the Composition Operators Preserving the Exponential Class |
| title_full | Explicit Bounds and Sharp Results for the Composition Operators Preserving the Exponential Class |
| title_fullStr | Explicit Bounds and Sharp Results for the Composition Operators Preserving the Exponential Class |
| title_full_unstemmed | Explicit Bounds and Sharp Results for the Composition Operators Preserving the Exponential Class |
| title_short | Explicit Bounds and Sharp Results for the Composition Operators Preserving the Exponential Class |
| title_sort | explicit bounds and sharp results for the composition operators preserving the exponential class |
| url | http://dx.doi.org/10.1155/2016/3769813 |
| work_keys_str_mv | AT fernandofarroni explicitboundsandsharpresultsforthecompositionoperatorspreservingtheexponentialclass AT raffaellagiova explicitboundsandsharpresultsforthecompositionoperatorspreservingtheexponentialclass |