T^{0,1}_p\n$. One can choose a basis $\L$ of $ T^{0,1}\n$ near the origin consisting of vector fields $L_j$ of the form

$$\label{e3} 
L_j={{\partial} \over {\partial \overline z_j}}+\sum_{\ell=1}^nF_{j
\ell} {{\partial} \over {\partial  s_{\ell}}}.$$

The wedge $\W$ in $\C^{k+m}$ with edge $\n$ on which we have holomorphic extension of the function $f$ in a neighborhood of the origin is of the form $$\W=\left (\U+i\Gamma\right ),$$ where $\U$ is a neighborhood of the origin in $\n$ and $\Gamma$ is a conic neighborhood of some vector $\mu$ in $\R^m\setminus
 \{0\}$. We make another linear change of variables, identifying the vector $\mu$ with $(1,1,...,1)$ thus not changing \[e2\]. We therefore have for some $\eta>0$ and $B_{\eta}(0)$, a ball centered at the origin in $\C^{k+m}$ of radius $\eta$

$$\label{e4}
 \begin{array}{l}
\W=\left (\U+i\Gamma\right ){\rm~~  ,where~} \U=B_{\eta}(0)\cap  \n~~
 {\rm and~} \Gamma~{\rm is~ a~conic~
 neighborhood~ of~}\\
 (1,1,....,1) ~{\rm in~} \R^m\setminus \{0\},\\
f~{\rm~extends~holomorphically~to~}\W=
 \left (\U+i\Gamma\right )\cap B_{\eta}(0).
\end{array}$$

Deformations
------------

Denote by $B_{r}$ the ball of radius $r$ centered at the origin in $\R^m$ and $\B_r$ the unit ball centered at the origin in $\C^k$. Let $d \in \R$ be such that for $\eta$ given by \[e4\] we have $$\label{e7}
0<d<{{\eta}\over {\sqrt m}}.$$ Let $\epsilon>0$ be given, let $\{b_j\}_{j=1}^m$ be 