Integral representations and embedding theorems for functions defined on the Heisenberg groups ℍⁿ

Romanovskiĭ, N.

doi:10.1090/S1061-0022-05-00854-X

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

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