We prove that on bounded domains Ω, the usual Sobolev inequality for sublaplacians on Carnot groups can be improved by adding a remainder term, in striking analogy with the euclidean case. We also show analogous results for subelliptic operators like script L sign = Δ x + |x| ^{2α} Δy, α > 0.
Sobolev inequalities with remaider terms for Sublaplacians and other subelliptic operators
LOIUDICE, ANNUNZIATA
2006-01-01
Abstract
We prove that on bounded domains Ω, the usual Sobolev inequality for sublaplacians on Carnot groups can be improved by adding a remainder term, in striking analogy with the euclidean case. We also show analogous results for subelliptic operators like script L sign = Δ x + |x| ^{2α} Δy, α > 0.File in questo prodotto:
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