Cauchy integral equalities and applications

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4 Citations (Scopus)

Abstract

We study bounded holomorphic functions n on the unit ball Bnof C satisfying the following so-called Cauchy integral equalities:for some sequence λmdepending on π. Among the applications are the Ahern-Rudin problem concerning the composition property of holomorphic functions on Bn, a projection theorem about the orthogonal projection of H2(Bn) onto the closed subspace generated by holomorphic polynomials in π, and some new information about the inner functions. In particular, it is shown that if we interpret BMOA(Bn) as the dual of H1(Bn), then the map g → g o π is a linear isometry of BMOA(B1) into BMOA(Bn) for every inner function π on Bnsuch that π(0) = 0.

Original languageEnglish
Pages (from-to)337-352
Number of pages16
JournalTransactions of the American Mathematical Society
Volume315
Issue number1
DOIs
Publication statusPublished - 1989 Sep

Keywords

  • Cauchy Integral Equalities
  • Projection
  • The Ahern-Rudin problem

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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