The p-Weil–Petersson Teichmüller Space and the Quasiconformal Extension of Curves

Abstract We consider the correspondence between space of p -Weil–Petersson curves $$\gamma $$ γ on plane and -Besov $$u=\log \gamma '$$ u = log ′ real line for $$p > 1$$ p > 1 . prove that variant Beurling–Ahlfors extension defined by using heat kernel yields a holomorphic map u domain to -integrable Beltrami coefficients. This in particular gives global real-analytic section Teichmüller projection from coefficients space.