Testing Schatten class Hankel operators, Carleson embeddings and weighted composition operators on reproducing kernels

Zen Harper, Martin P. Smith

Research output: Contribution to journalArticlepeer-review

Abstract

Given an operator A on a Hilbert space H and c G H, we consider operators Lambda(A,c) defined on analytic functions f by Lambda(A,c)f = f (A)c. Special cases of Lambda(A,c) include vectorial Hankel operators, Carleson embeddings and weighted composition operators. For certain A, we determine conditions under which Lambda(A,c) extends to an operator of Schatten von-Neumann class on the Hardy or Bergman space of the disc. These conditions involve only the action of Lambda(A,c) on reproducing kernels and their derivatives. We also give corresponding results for operators on the Hardy space of the half-plane.

Original languageEnglish
Pages (from-to)349-371
Number of pages23
JournalJournal of Operator Theory
Volume55
Issue number2
Publication statusPublished - 2006

Keywords

  • Schatten classes
  • reproducing kernels
  • Hardy space
  • Bergman space
  • Hankel operators
  • Carleson embeddings
  • composition operators
  • WEISS CONJECTURE

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