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Singular functions on metric measure spaces.

Ilkka HolopainenNageswari Shanmugalingam — 2002

Collectanea Mathematica

On relatively compact domains in metric measure spaces we construct singular functions that play the role of Green functions of the p-Laplacian. We give a characterization of metric spaces that support a global version of such singular function, in terms of capacity estimates at infinity of such metric spaces. In addition, when the measure of the space is locally Q-regular, we study quasiconformal invariance property associated with the existence of global singular functions.

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