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Essential norm of integral type operators mapping into certain Banach spaces of analytic functions. (English) Zbl 1441.30087

Summary: We study certain integral type operators acting on a large class of Banach spaces of analytic functions on the open unit disc. The operators map into weighted Banach spaces of analytic functions, Bloch type spaces or Zygmund type spaces. Besides characterizing boundedness, we give essential norm estimates of these operators. In order to investigate these operators, we also study weighted differentiation composition operators between these spaces.

MSC:

30H99 Spaces and algebras of analytic functions of one complex variable
47B38 Linear operators on function spaces (general)
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