Fredrik Brevig, OleOrtega Cerdà, JoaquimSeip, Kristian2021-02-032023-01-062021-01-060022-247Xhttps://hdl.handle.net/2445/173610A 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.application/pdfengcc-by-nc-nd (c) Elsevier, 2021http://creativecommons.org/licenses/by-nc-nd/3.0/esEspais de HardyAnàlisi harmònicaHardy spacesHarmonic analysisinfo:eu-repo/semantics/article7054472021-02-03info:eu-repo/semantics/openAccess