EXTENSION AND RESTRICTION FOR BERGMAN SCALE OF SPACES AND ONE-DIMENSIONAL SUBVARIETIES ON CONVEX FINITE TYPE DOMAINS

We prove that the extension problem from one-dimensional subvarieties with values in Bergman space $H^{1}(D)$ on convex finite type domains can be solved by means of appropriate measures. We obtain also almost optimal results concerning the extension problem for other Bergman spaces and one-dimensional varieties.