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Partial differential equations with non-Euclidean geometries

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  • 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.
    Mathematics Subject Classification: Primary: 45E10, 35J15; Secondary: 35Q30.


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