Marcinkiewicz-Zygmund Inequalities for Polynomials in Bergmann and Hardy Spaces

TL;DR

This paper investigates Marcinkiewicz-Zygmund inequalities within Hardy and Bergman spaces, analyzing sampling sequences and polynomial subspaces to understand their differing behaviors in these classical function spaces.

Contribution

It establishes new relationships between sampling sequences and inequalities in Hardy and Bergman spaces, highlighting their contrasting properties in one-variable settings.

Findings

Different behaviors of Hardy and Bergman spaces analyzed

Relationships between sampling sequences and inequalities clarified

Insights into polynomial subspaces in analytic function spaces

Abstract

We study the relationship between sampling sequences in infinite dimensional Hilbert spaces of analytic functions and Marcinkiewicz-Zygmund inequalities in subspaces of polynomials. We focus on the study of the Hardy space and the Bergman space in one variable because they provide two settings with a strikingly different behavior.