A converse to the Schwarz lemma for planar harmonic maps

Abstract

A sharp version of a recent inequality of Kovalev and Yang on the ratio of the $(H^1{)}^{\ast }$ and $H^4$ norms for certain polynomials is obtained. The inequality is applied to establish a sharp and tractable sufficient condition for the Wirtinger derivatives at the origin for harmonic self-maps of the unit disc which fix the origin.

arXiv commentOne typo corrected. This paper has been accepted for publication in Journal of Mathematical Analysis and Applications

References in corpus (3)

• Contractive inequalities for Hardy spaces
• Near-isometric duality of Hardy norms with applications to harmonic mappings
• Linear functions and duality on the infinite polytorus

Cited by in corpus (1)

• Schwarz-Pick lemma for harmonic maps which are conformal at a point