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Trudinger‐Moser inequalities on the entire Heisenberg group
Author(s) -
Yang Yunyan
Publication year - 2014
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.201200019
Subject(s) - heisenberg group , mathematics , euclidean space , euclidean geometry , group (periodic table) , mathematical proof , pure mathematics , domain (mathematical analysis) , class (philosophy) , space (punctuation) , inequality , argument (complex analysis) , algebra over a field , mathematical analysis , geometry , epistemology , philosophy , chemistry , linguistics , organic chemistry , biochemistry
Continuing our previous work (Cohn, Lam, Lu, Yang, Nonlinear Analysis, 2011), we obtain a class of Trudinger‐Moser inequalities on the entire Heisenberg group, which indicate what the best constants are. All the existing proofs of similar inequalities on unbounded domain of the Euclidean space or the Heisenberg group are based on rearrangement argument. In this note, we propose a new approach to solve this problem. Specifically we get the global Trudinger‐Moser inequality by gluing local estimates with the help of cut‐off functions. Our method still works for similar problems when the Heisenberg group is replaced by the Euclidean space or complete noncompact Riemannian manifolds.