English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We show that if an open arc J of the boundary of a Jordan domain $${\varOmega }$$ Ω is rectifiable, then the derivative $$\varPhi '$$ Φ ′ of the Riemann map $$\varPhi :D\;\rightarrow \;{\varOmega }$$ Φ : D → Ω from the open unit disk D onto $${\varOmega }$$ Ω behaves as an $$H^1$$ H 1 function when we approach the arc $$\varPhi ^{-1}(J')$$ Φ - 1 ( J ′ ) , where $$J'$$ J ′ is any compact subarc of J . Nous démontrons que si un arc ouvert J de la frontière d’ un domaine de Jordan $$\varOmega $$ Ω est rectifiable, alors la dérivée $$\varPhi ^{\prime }$$ Φ ′ de la fonction de Riemann $$\varPhi $$ Φ entre le disque unité ouvert D sur $$\varOmega $$ Ω se comporte comme une fonction de classe de Hardy $$H^1$$ H 1 , quand on approche le sous-ensemble $$\varPhi ^{-1}(J^{\prime })$$ Φ - 1 ( J ′ ) où $$J^{\prime }$$ J ′ est un sous-ensemble compact de J .

Jordan domains with a rectifiable arc in their boundary