Müntz spaces and special Bloch type inequalities

Abstract

In this paper, we are interested in classical Müntz spaces and their properties. We first reprove Müntz theorem and obtain the Clarkson–Erdös–Schwartz expansion in the nondense case for some general abstract Müntz spaces without invoking any blow up property, but using classical complex variables tools. We introduce new Bloch type Müntz spaces and investigate the validity of Bloch type inequalities in this framework.

Keywords:

• Müntz spaces
• Power series
• lacunary sequences
• Bloch type inequalities

AMS Subject Classification:

• 30B10

Acknowledgements

We wish to thank the referee for her/his suggestions in order to improve the quality of this paper.

Notes

No potential conflict of interest was reported by the author.