Boundary behaviour of the mappings satisfying generalized inverse modular inequalities

Abstract

We study the geometric properties of the mappings for which generalized inverse modular inequalities hold. We generalize in this way known theorems from the theory of analytic mappings and the theory of quasiregular mappings, like the theorems of Fatou, M. and F. Riesz, Beurling and Lindelöf and their extensions given for quasiregular mappings by Martio, Rickman and Vuorinen.

Keywords:

• quasiregular mappings
• analytic mappings
• generalizations of quasiregular mappings
• boundary behavior of Sobolev mappings

AMS Subject Classification:

• 30C65

Acknowledgements

We thank the referees for their comments.