Let Apdenote the class of holomorphic functions on the unit disc whose first p-derivatives belong to the disc algebra. We characterize the boundary interpolation sets for Apthat is, those closed sets E Ì T such that every function inCP(E) extends to a function in ApWe also give a constructive proof of the corresponding result for A¥(see ). We show that the structure of these sets is in some sense related to BMO and that this fact can be used to obtain precise estimates of outer functions vanishingon E. © 1981 American Mathematical Society.
|Journal||Transactions of the American Mathematical Society|
|Publication status||Published - 1 Jan 1981|
- Boundary interpolation sets
- Carleson sets
- Lipschitz conditions
- Outer functions