By Prof. Dr. Gennadi M. Henkin, Prof. Dr. Jürgen Leiterer (auth.)

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**Example text**

We aay aD ia piecewise almost Cl if there exist a neighborhood U of aD and a finite number of closed almost c 1 hypersurfaces Y1 , ... ,YN in U (of. Sect. 1) such that the following conditions are fulfilled: 46 u N aD= ( i) YjnoD; j=l (ii) for all l~i

K 1 ~N. 8) For any bounded differential form f on SK' by (L~f)(z) = we define a continuous differential form L~f in D. "v = (LK)r(z,x,t) (O~r~n-1) we denote the sum of all monomials are of bidegree (O,r) in z. 9) for r=O, ... , n-1. 6. Proposition. Let D ~ Cn be a domain with piecewise almost c1 boundary, Y=(Y 1 , ... ,YN) a frame forD, v a Leray map for (D,Y), and K=(k 1 , ... ,k 1 ) a strictly increasing collection of integers 1~k 1 < ...

The Cauchy-Fantappie integral Lv. Let D cc ~n be a domain with almost c 1 boundary, and let v be a Leray map for D. :J(x) L (z,x) = - 1( 2 ll:i)n \ z,x ~v ( 2. 1) for Z€D and xeoD, and for any bounded differential form f on oD, by I f(x)ALv(z,x), X€aD we define a continuous differential form Lvf in D. 2) By Lv=Lv(z,x) (O