On Bojarski’s Index Formula for Nonsmooth Interfaces

Let D be a Dirac type operator on a compact manifold M and let Σ be a Lipschitz submanifold of codimension one partitioningM into two Lipschitz domains Ω±. Also, let Hp±(Σ, D) be the traces on Σ of the (Lpstyle) Hardy spaces associated with D in Ω±. Then (Hp−(Σ, D),Hp+(Σ, D)) is a Fredholm pair of subspaces for Lp(Σ) (in Kato’s sense) whose index is the same as the index of the Dirac operator D considered on the whole manifold M.