# American Institute of Mathematical Sciences

September  2008, 1(3): 481-504. doi: 10.3934/dcdss.2008.1.481

## Partial differential equations with non-Euclidean geometries

 1 Mathematisches Institut, Universität Bonn, Beringstrasse 1, D - 53115 Bonn, Germany

Received  February 2008 Revised  March 2008 Published  June 2008

Coifman and Weiss initiated the study of singular integral operators on spaces of homogeneous type. We study partial differential equations with a non-Euclidean geometry and we obtain weighted estimates using the theory of Muckenhoupt weights on related spaces of homogeneous type. Examples include squares of vector fields, elliptic operators with a drift and the Oseen operator.
Citation: Herbert Koch. Partial differential equations with non-Euclidean geometries. Discrete & Continuous Dynamical Systems - S, 2008, 1 (3) : 481-504. doi: 10.3934/dcdss.2008.1.481
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