English

A converse to the Schwarz lemma for planar harmonic maps

Complex Variables 2021-01-12 v2

Abstract

A sharp version of a recent inequality of Kovalev and Yang on the ratio of the (H1)(H^1)^\ast and H4H^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.

Keywords

Cite

@article{arxiv.2011.10967,
  title  = {A converse to the Schwarz lemma for planar harmonic maps},
  author = {Ole Fredrik Brevig and Joaquim Ortega-Cerdà and Kristian Seip},
  journal= {arXiv preprint arXiv:2011.10967},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-23T20:25:22.862Z