Envelope of holomorphy for boundary cross sets
Abstract
Description
Let $D\subset \C^n,$ $G\subset \C^m$ be open sets, let
$A$ (resp. $B$) be a subset of the boundary $\partial D$ (resp.
$\partial G$) and let $W$ be the 2-fold boundary cross $((D\cup A)\times B)\cup (A\times(B\cup G)).$
An open subset $X\subset\C^{n+m} $ is said to be the ``envelope of holomorphy" of $W$ if it is, in some sense, the maximal open set with the following property: Any function locally bounded on $W$ and separately holomorphic on $(A\times G) \cup (D\times B)$ "extends" to a holomorphic function defined on $X$ which admits the boundary values $f$ a.e. on $W.$ In this work we will determine the envelope of holomorphy of some boundary crosses.
Arch. Math. (Basel), to appear, 12 pages
Arch. Math. (Basel), to appear, 12 pages