Gain of Regularity in Extension Problem on Convex Domains

Abstract EN

We investigate the extension problem from higher codimensional linear subvarieties on convex domains of finite type.

We prove that there exists a constant d such that on Bergman spaces H p ( D ) with 1 ≤ p < d there appears the so-called “gain regularity.” The constant d depends on the minimum of the dimension and the codimension of the subvariety.

This means that the space of functions which admit an extension to a function in the Bergman space H p ( D ) is strictly larger than H p ( D ∩ A ) , where A is a subvariety.