Carleson Measure of Harmonic Schwarzian Derivatives Associated with a Finitely Generated Fuchsian Group of the Second Kind. (22nd March 2021) - Hu, Guangming; Liu, Yutong; Sun, Yu; Qian, Xinjie
Abstract : Let S H f be the Schwarzian derivative of a univalent harmonic function f in the unit disk D, compatible with a finitely generated Fuchsian group G of the second kind. We show that if S H f 2 1 − z 2 3 d x d y satisfies the Carleson condition on the infinite boundary of the Dirichlet fundamental domain F of G, then S H f 2 1 − z 2 3 d x d y is a Carleson measure in D .