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Example text

Notice that, of course, any Leraydatumw(z,x) leads to the Leray ~ v(z,x):= w(z,x)/(x-z). In Sect. 4 we shall consider generalizations of both the notion of a Leray data and the notion of a Leray map. Then the difference between them becomes more substantial. 2. 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.

0 ° 2. 1. Leray data and Leray maps. Let D cc Cn be a domain with almost boundary. A en-valued c 1 map v=(v 1 , ... ,vn) defined on DxaD will be called a Leraydatum for D if f 0 for all zED and x£oD. D and XEOD, c1 If, moreover, then v will be called a Leray ~ for D. Remark. In [H/L] the notion of a Leray ~ is used for arbitrary Leray data . Notice that, of course, any Leraydatumw(z,x) leads to the Leray ~ v(z,x):= w(z,x)/(x-z). In Sect. 4 we shall consider generalizations of both the notion of a Leray data and the notion of a Leray map.

N). 7) for any strictly increasing collection K=(k 1 , ... ,k1 ) of integers 1~k 1 < ...

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