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Integral representations and embedding theorems for functions defined on the Heisenberg groups  $\mathbb H^n$


Author: N. N. Romanovskii
Translated by: B. M. Bekker
Original publication: Algebra i Analiz, tom 16 (2004), nomer 2.
Journal: St. Petersburg Math. J. 16 (2005), 349-375
MSC (2000): Primary 46E35
DOI: https://doi.org/10.1090/S1061-0022-05-00854-X
Published electronically: March 9, 2005
MathSciNet review: 2068343
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Abstract | References | Similar Articles | Additional Information

Abstract: Integral representations of Sobolev type are obtained for functions defined on the Heisenberg group $\mathbb H^n$. These representations are employed to prove embedding theorems, Poincaré inequalities, and coercive estimates for functions defined on regions in $\mathbb H^n$.


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Additional Information

N. N. Romanovskii
Affiliation: Sobolev Institute of Mathematics, Siberian Branch of RAS, Akademika Koptyuga 4, Novosibirsk 630090, Russia
Email: nnrom@math.nsc.ru

DOI: https://doi.org/10.1090/S1061-0022-05-00854-X
Keywords: Heisenberg groups, Sobolev spaces, integral representations, embedding theorems, coercive estimates
Received by editor(s): February 19, 2003
Published electronically: March 9, 2005
Additional Notes: Partially supported by RFBR (grants nos. 97-01-01092 and 96-15-96291) and by INTAS-10170
Article copyright: © Copyright 2005 American Mathematical Society

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