Abstract
This paper deals with the pull-back operator on the real-valued harmonic Dirichlet space by a quasisymmetric function. A new metric on Teichmüller spaces is defined and discussed. The results turn out to be closely related to some important functionals in complex analysis and some invariant metrics on Teichmüller spaces. As by-products, we can reprove some important results obtained by Krushkal.
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