Univalent functions and Dirichlet-Morrey spaces

Abstract

This paper concerns univalent analytic functions f for which $\log f^{\prime }$ belong to Dirichlet-Morrey spaces. We establish some characterizations of Dirichlet-Morrey domains. Our results involve Schwarzian derivatives, quasiconformal extensions and Grunsky kernels of univalent functions.

Keywords:

• Univalent function
• Schwarzian derivative
• logarithmic derivative
• quasiconformal map
• Dirichlet-Morrey space

AMS SUBJECT CLASSIFICATIONS:

• Primary 47B33
• 46E15
• 30D50

Acknowledgments

The authors would like to thank the referee for the useful suggestions that helped to improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was financially supported by National Natural Science Foundation of China (Grant No. 11601100 11501157), the joint foundation of Guizhou Provincial Science and Technology Department (Grant No. [2017]7337), Research projects of Young and Middle-aged Teacher's Education of Fujian Province (Grant No. JAT190508), Scientific Research Project of Quanzhou Normal University (Grant No. H19009), PHD Research Startup Foundation of Jinling Institute of Technology (Grant No. jit-b-202011).