Contractive inequalities for Hardy spaces

Abstract

We state and discuss several interrelated results, conjectures, and questions regarding contractive inequalities for classical $H^p$ spaces of the unit disc. We study both coefficient estimates in terms of weighted ${\ell }^2$ sums and the Riesz projection viewed as a map from $L^q$ to $H^p$ with $q\ge p$. Some numerical evidence is given that supports our conjectures.

This paper has been accepted for publication in Functiones et Approximatio Commentarii Mathematici

References in corpus (2)

• An inequality of Hardy--Littlewood type for Dirichlet polynomials
• Pseudomoments of the Riemann zeta function

Cited by in corpus (9)

• Hypercontractive inequalities for weighted Bergman spaces
• A monotonicity theorem for subharmonic functions on manifolds
• Point evaluation in Paley--Wiener spaces
• A converse to the Schwarz lemma for planar harmonic maps
• Contractive inequalities for mixed norm spaces and the Beta function
• Linear functions and duality on the infinite polytorus
• A contractive Hardy-Littlewood inequality
• Coefficient estimates for $H^p$ spaces with $0<p<1$
• Critical exponents of the Riesz projection