© 2013

Derivatives of Inner Functions


Part of the Fields Institute Monographs book series (FIM, volume 31)

Table of contents

  1. Front Matter
    Pages i-x
  2. Javad Mashreghi
    Pages 1-26
  3. Javad Mashreghi
    Pages 27-38
  4. Javad Mashreghi
    Pages 39-50
  5. Javad Mashreghi
    Pages 51-70
  6. Javad Mashreghi
    Pages 71-81
  7. Javad Mashreghi
    Pages 83-97
  8. Javad Mashreghi
    Pages 99-124
  9. Javad Mashreghi
    Pages 125-143
  10. Javad Mashreghi
    Pages 145-155
  11. Javad Mashreghi
    Pages 157-166
  12. Back Matter
    Pages 167-169

About this book


Derivatives of Inner Functions was inspired by a conference held at the Fields Institute in 2011 entitled "Blaschke Products and Their Applications." Inner functions form an important subclass of bounded analytic functions. Since they have unimodular boundary values, they appear in many extremal problems of complex analysis. They have been extensively studied since the early twentieth century and the literature on this topic is vast. This book is devoted to a concise study of derivatives of inner functions and is confined to treating the integral means of derivatives and presenting a comprehensive list of results on Hardy and Bergman means.

This self-contained monograph allows researchers to get acquainted with the essentials of inner functions, rendering this theory accessible to graduate students while providing the reader with rapid access to the frontiers of research in this field.


Bergman spaces Blaschke products Caratheodory derivative bounded analytic functions integral means

Authors and affiliations

  1. 1., Département de mathématiques et de statiUniversité LavalQuebecCanada

Bibliographic information


From the reviews:

“This short monograph presents an account with full proofs of early investigations from around 1970–1980 on derivatives of inner functions … . the author also revisits Carathéodory’s theory on angular derivatives and gives a brief glimpse on Frostman’s results on exceptional sets for inner functions. … It fits well for student seminars.” (Raymond Mortini, Mathematical Reviews, August, 2013)