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The G ‐Ellipticity for the Sub‐Laplacian on Two Step Stratified Lie Groups
Author(s) -
Jiang Yaping
Publication year - 1996
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.3211810109
Subject(s) - mathematics , laplace operator , lie group , elliptic operator , pure mathematics , invariant (physics) , euclidean space , euclidean geometry , p laplacian , operator (biology) , mathematical analysis , mathematical physics , geometry , boundary value problem , biochemistry , chemistry , repressor , transcription factor , gene
This paper reveals that the sub‐Laplacian L 0 on two step stratified Lie groups has a similar behavior like elliptic operators on the Euclidean space, that is, the sub ‐ Laplacian satisfies a group‐elliptic estimate, called the G ‐ elliptic estimate (or the L p regularity), and the general left Invariant operator L λ has such a behavior if and only if λ is admissible.