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

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Publication details

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

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.

    Research areas

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

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