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Sobolev Inequalities and Harmonic Functions of Polynomial Growth
Author(s) -
Alexopoulos G.,
Lohoué N.
Publication year - 1993
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-48.3.452
Subject(s) - mathematics , polynomial , harmonic function , inequality , sobolev inequality , sobolev space , pure mathematics , lie group , mathematical analysis
We prove a Sobolev inequality for functions not necessarily with compact support, on a connected Lie group G of polynomial volume growth. To prove this inequality we have to characterise the harmonic functions of polynomial growth on G .