Interpolating sequences and Carleson measures in the Hardy-Sobolev spaces of the ball in $C^n$

TL;DR

This paper investigates Hardy-Sobolev spaces in the unit ball of complex n-space, focusing on interpolating sequences and Carleson measures, and compares these with classical Hardy spaces to highlight key similarities and differences.

Contribution

It provides a detailed analysis of interpolating sequences and Carleson measures in Hardy-Sobolev spaces, establishing their relation to classical Hardy spaces in several complex variables.

Findings

Characterization of interpolating sequences in Hardy-Sobolev spaces

Comparison of Carleson measures between Hardy-Sobolev and classical Hardy spaces

Identification of key analogies and differences in space properties

Abstract

In this work we study Hardy Sobolev spaces in the ball of $C^n$ with respect to interpolating sequences and Carleson measures. We compare them with the classical Hardy spaces of the ball and we stress analogies and differences.