EXTENSION OF HOLOMORPHIC-FUNCTIONS

We study the extension of holomorphic functions defined on a pion necessarily transverse subvariety of the real or complex ellipsoid. If the data has given regularity in L(p) norm With 1 less than or equal to p less than or equal to +infinity, we describe the regularity of the extension. We show that the regularity decay depends on the interaction between the complex geometry of the ellipsoid boundary and the given subvariety, although the Cauchy-Riemann equation can be solved in ellipsoids with some gain of regularity.