Quasiconformal mappings and Sobolev spaces

• Autorzy: Pekka Koskela , Paul MacManus
• Języki publikacji: EN

Abstrakty

EN

We examine how Poincaré change under quasiconformal maps between appropriate metric spaces having the same Hausdorff dimension. We also show that for many metric spaces the Sobolev functions can be identified with functions satisfying Poincaré, and this allows us to extend to the metric space setting the fact that quasiconformal maps from $ℝ^Q$ onto $ℝ^Q$ preserve the Sobolev space $L^{1,Q}(ℝ^Q)$.

Kategorie tematyczne

• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 30C65: Quasiconformal mappings in 𝐑 n , other generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 131
• Numer: 1
• Strony: 1-17

Daty

wydano

1998

otrzymano

1997-04-01

Twórcy

autor

Pekka Koskela

• University of Jyväskylä, Department of Mathematics, P.O. Box 35, Fin-40351 Jyväskylä, Finland

autor

Paul MacManus

• Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
• Permanent address: Department of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland

Bibliografia

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