IJPAM: Volume 1, No. 2 (2002)

THE RUDIN-CARLESON THEOREM FOR
NON-HOMOGENEOUS DIFFERENTIAL FORMS

Angelica Malaspina
Dept. of Mathematics
University of Basilicata
C/da Macchia Romana, Potenza, 85100, ITALY
e-mail: malaspina@pzmath.unibas.it


Abstract.Let $\O$ be a bounded domain of $\R^n$ such that its boundary is a Lyapunov hypersuface $\S$ and $\R^n - \overline\O$ is connected. It is proved that if $\S$ is a closed subset of $(n-1)$-dimensional Lebesgue zero measure on $\S$, and if $f$ and $\ti f$ are continuous non-homogeneous differential forms on $\S$, then there exists a non-homogeneous differential form $U$ on $\O$ which is self-conjugate in $\O$ and such that $U$ and its adjoint form extend $f$ and $\ti f$ respectively. This result holds for any $n\geq 2$ and it generalizes the classical Rudin-Carleson theorem.

Received: February 2, 2002

AMS Subject Classification: 58A10, 31B25, 46N20

Key Words and Phrases: Rudin-Carleson theorem, differential forms

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 1
Issue: 2