Multi-point bounds for analytic functions under measure conditions

Abstract

Let be an analytic function on the unit disc with image satisfying a measure condition. We prove an upper and a lower bound for the modulus for every involving all the pre-images of

Keywords:

• angular domains
• circular symmetrization
• Green function
• Littlewood Theorem
• measure conditions
• Schwarz lemma

AMS Subject Classifications:

• 30C25
• 30C80
• 30C85
• 31A15

Acknowledgements

The first-named author would like to thank the Cyprus State Scholarship Foundation for its support. The content of the paper was carried out while the second-named author was a postdoctoral associate of University of Cyprus. The authors would like to thank the referee for his remarks and especially for his suggestion to compare their result with a theorem of Mityuk [12].