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Let $D$ be a Dirac type operator on a compact manifold ${\mathcal{M}}$ and let $\Sigma $ be a Lipschitz submanifold of codimension one partitioning ${\mathcal{M}}$ into two Lipschitz domains $\Omega _{\pm }$. Also, let ${\mathcal{H}}^{p}_{\pm }(\Sigma ,D)$ be the traces on $\Sigma $ of the ($L^{p}$-style) Hardy spaces associated with $D$ in $\Omega _{\pm }$. Then $({\mathcal{H}}^{p}_{-}(\Sigma ,D),{\mathcal{H}}^{p}_{+}(\Sigma ,D))$ is a Fredholm pair of subspaces for $L^{p}(\Sigma )$ (in Kato's sense) whose index is the same as the index of the Dirac operator $D$ considered on the whole manifold ${\mathcal{M}}$.

Copyright 1999 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 05 (1999), pp. 40-46
• Publisher Identifier: S 1079-6762(99)00060-8
• 1991 Mathematics Subject Classification. Primary 58G10, 42B20
• Key words and phrases.
• Received by the editors December 02, 1998
• Posted on April 6, 1999
• Communicated by Stuart Antman
• Comments (When Available)

Marius Mitrea

Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211

E-mail address: marius@math.missouri.edu