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.
@article{urn:eudml:doc:42987,
title = {Singular functions on metric measure spaces.},
journal = {Collectanea Mathematica},
volume = {53},
year = {2002},
pages = {313-332},
zbl = {1039.31016},
mrnumber = {MR1940332},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42987}
}
Holopainen, Ilkka; Shanmugalingam, Nageswari. Singular functions on metric measure spaces.. Collectanea Mathematica, Tome 53 (2002) pp. 313-332. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42987/