Contractive inequalities between Dirichlet and Hardy spaces

TL;DR

This paper proves a conjecture relating Dirichlet and Hardy spaces through contractive inequalities and explores its implications for the Riesz projection.

Contribution

It establishes a new contractive inequality between Dirichlet and Hardy spaces, confirming a conjecture and linking it to the Riesz projection.

Findings

Proved the conjecture on inequalities between Dirichlet and Hardy spaces

Connected the inequality to properties of the Riesz projection

Enhanced understanding of space relationships in complex analysis

Abstract

We prove a conjecture of Brevig, Ortega-Cerd\`a, Seip and Zhao about contractive inequalities between Dirichlet and Hardy spaces and discuss its consequent connection with the Riesz projection.