ON THE UNIFORM APPROXIMATION PROBLEM FOR THE SQUARE OF THE CAUCHY-RIEMANN OPERATOR

Let X be a compact subset of the plane and f a continuous function on X satisfying the equation partial derivative2BAR f = 0 in the interior of X . It is unknown whether f can be uniformly approximated on X by functions g satisfying the equation partial derivative2BAR g = 0 in so me neighbourhood (depending on g) of X. We show that this is the case under the additional assumption that f satisfies a Dini-type continuit y condition.