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Contractive inequalities between Dirichlet and Hardy spaces

Adrián Llinares

Abstract

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

Contractive inequalities between Dirichlet and Hardy spaces

Abstract

We prove a conjecture of Brevig, Ortega-Cerdà, Seip and Zhao about contractive inequalities between Dirichlet and Hardy spaces and discuss its consequent connection with the Riesz projection.
Paper Structure (4 sections, 7 theorems, 37 equations)

This paper contains 4 sections, 7 theorems, 37 equations.

Table of Contents

  1. Introduction
  2. Proof of Conjecture \ref{['BOSZ']}
  3. Extension to several variables and Dirichlet series
  4. Contractive inequalities for the Riesz projection

Key Result

Theorem A

Let $0 < p < q$ and $-1 \leq \alpha < \beta$ such that $\frac{\alpha + 2}{p} = \frac{\beta + 2}{q}$. Then we have that and equality is possible if and only if there exists $\zeta \in \mathbb{D}$ and $C \in \mathbb{C}$ such that

Theorems & Definitions (13)

  • Theorem A
  • Corollary 1.1
  • proof
  • Conjecture B
  • Theorem 2.1
  • proof
  • Corollary 2.2
  • proof
  • Theorem 3.1
  • Corollary 3.2
  • ...and 3 more