Tangential interpolation in weighted vector-valued H^p spaces, with applications

TL;DR

This paper derives norm estimates for tangential interpolation in weighted vector-valued H^p spaces using Carleson measures, with applications to controllability in linear systems and Sobolev spaces.

Contribution

It introduces new norm estimates for minimal-norm tangential interpolation in weighted H^p spaces, linking them to Carleson constants and applications in control theory.

Findings

Norm estimates expressed via Carleson constants.

Applications to p-controllability of linear semigroup systems.

Controllability results using Sobolev space functions.

Abstract

In this paper, norm estimates are obtained for the problem of minimal-norm tangential interpolation by vector-valued analytic functions in weighted H^p spaces, expressed in terms of the Carleson constants of related scalar measures. Applications are given to the notion of p-controllability properties of linear semigroup systems and controllability by functions in certain Sobolev spaces.