Integral representations and embedding theorems for functions defined on the Heisenberg groups $\mathbb H^n$
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N. N. Romanovskiĭ
Translated by: B. M. Bekker - St. Petersburg Math. J. 16 (2005), 349-375
- DOI: https://doi.org/10.1090/S1061-0022-05-00854-X
- Published electronically: March 9, 2005
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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 $\mathbb H^n$.References
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Bibliographic Information
- N. N. Romanovskiĭ
- Affiliation: Sobolev Institute of Mathematics, Siberian Branch of RAS, Akademika Koptyuga 4, Novosibirsk 630090, Russia
- Email: nnrom@math.nsc.ru
- 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
- © Copyright 2005 American Mathematical Society
- Journal: St. Petersburg Math. J. 16 (2005), 349-375
- MSC (2000): Primary 46E35
- DOI: https://doi.org/10.1090/S1061-0022-05-00854-X
- MathSciNet review: 2068343