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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-8896 2314-8888 |