# Singular functions on metric measure spaces.

Ilkka Holopainen; Nageswari Shanmugalingam

Collectanea Mathematica (2002)

- Volume: 53, Issue: 3, page 313-332
- ISSN: 0010-0757

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topHolopainen, Ilkka, and Shanmugalingam, Nageswari. "Singular functions on metric measure spaces.." Collectanea Mathematica 53.3 (2002): 313-332. <http://eudml.org/doc/42987>.

@article{Holopainen2002,

abstract = {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.},

author = {Holopainen, Ilkka, Shanmugalingam, Nageswari},

journal = {Collectanea Mathematica},

keywords = {Función singular; Función de Green; Mapeo; Función armónica; Espacio de medida; Espacios métricos; Green functions; -harmonic functions; -capacity; quasiconformal mappings; hyperbolicity},

language = {eng},

number = {3},

pages = {313-332},

title = {Singular functions on metric measure spaces.},

url = {http://eudml.org/doc/42987},

volume = {53},

year = {2002},

}

TY - JOUR

AU - Holopainen, Ilkka

AU - Shanmugalingam, Nageswari

TI - Singular functions on metric measure spaces.

JO - Collectanea Mathematica

PY - 2002

VL - 53

IS - 3

SP - 313

EP - 332

AB - 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.

LA - eng

KW - Función singular; Función de Green; Mapeo; Función armónica; Espacio de medida; Espacios métricos; Green functions; -harmonic functions; -capacity; quasiconformal mappings; hyperbolicity

UR - http://eudml.org/doc/42987

ER -

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