An embedding constant for the Hardy space of Dirichlet series

TL;DR

This paper provides a new, straightforward proof for embedding the Hardy--Hilbert space of Dirichlet series into a conformally invariant Hardy space, and calculates the optimal embedding constant.

Contribution

It introduces a simple proof for the embedding and determines the optimal constant, advancing understanding of Hardy spaces of Dirichlet series.

Findings

Embedding constant explicitly computed

Simplified proof of the embedding established

Optimal constant identified

Abstract

A new and simple proof of the embedding of the Hardy--Hilbert space of Dirichlet series into a conformally invariant Hardy space of the half-plane is presented, and the optimal constant of the embedding is computed.