Coefficient multipliers on Banach spaces of analytic functions

  • Óscar Blasco

    Universidad de Valencia, Spain
  • Miroslav Pavlović

    University of Belgrade, Beograd, Serbia

Abstract

Motivated by an old paper of Wells [J. London Math. Soc. {\bf 2} (1970), 549-556] we define the space , where and are "homogeneous" Banach spaces of analytic functions on the unit disk , by the requirement that can be represented as , with , and . We show that this construction is closely related to coefficient multipliers. For example, we prove the formula , where denotes the space of multipliers from to , and as a special case , where . We determine for a class of spaces that contains and , and use this together with the above formulas to give quick proofs of some important results on multipliers due to Hardy and Littlewood, Zygmund and Stein, and others.

Cite this article

Óscar Blasco, Miroslav Pavlović, Coefficient multipliers on Banach spaces of analytic functions. Rev. Mat. Iberoam. 27 (2011), no. 2, pp. 415–447

DOI 10.4171/RMI/642