Structure of free interpolation sets for analytic function spaces determined by a modulus of continuity

A. M. Kotochigov

Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 30, Tome 290 (2002), pp. 122-137

Résumé

We describe how of boundary interpolation sets changes between the disk-algebra and Hölder spaces of analytic functions. For the disk-algebra, an interpolation set is a set of zero measure, and for Hölder classes of order $\alpha$ it is a porous set. For the Hölder-type classes corresponding to a modulus of continuity $\omega$, a certain condition of $\omega$-porosity turnes out to be necessary for free interpolation. Every set of zero measure is $\omega$-porous for some $\omega$.We prove also a Muckehoupt-type inequality that may be of use for the proof of the sufficiency of the $\omega$-porosity condition.