A kind of edge of the wedge theorem is studied, generalizing the Hardy spaces on tube domains. For an open subset of , and , let and define the space , by the set of all functions f which are holomorphic on and satisfy, for some r, ,
for . Then the main theorem is as follows: Let C be an open cone in which is the union of a finite number of open convex cones , such that contains interior points and a basis in . Here O(C) is the convex hull of C and * denotes the operation of taking dual cone. Suppose , , and the boundary values of in (as in , corresponding to each connected component of C are equal in . Then there is an F which is holomorphic on and in , where F has the form , , with P(z) being a polynomial in z and
a constant depending on C.