Sharp bounds for composition with quasiconformal mappings in Sobolev spaces

Journal of Mathematical Analysis and Applications（2017）

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摘要

Let ϕ be a quasiconformal mapping, and let Tϕ be the composition operator which maps f to f∘ϕ. Since ϕ may not be bi-Lipschitz, the composition operator need not map Sobolev spaces to themselves. The study begins with the behavior of Tϕ on Lp and W1,p for 1更多

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关键词

Sobolev spaces,Fractional smoothness,Quasiconformal mappings,Composition operator

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