  This article discusses questions in one and several complex variables about
the size of the sum of the moduli of the terms of the series expansion of a
bounded holomorphic function. Although the article is partly expository, it
also includes some previously unpublished results with complete proofs.
  The article is based on a lecture at the third Korean several complex
variables symposium held at the Global Analysis Research Center at Seoul
National University in December 1998.
