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On Bojarski's index formula for nonsmooth interfaces
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## On Bojarski's index formula for nonsmooth interfaces

### Marius Mitrea

**Abstract.**
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`

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