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Level sets and Composition operators on the Dirichlet space

Abstract : We consider composition operators in the Dirichlet space of the unit disc in the plane. Various criteria on boundedness, compactness and Hilbert-Schmidt class membership are established. Some of these criteria are shown to be optimal.
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Submitted on : Wednesday, March 24, 2010 - 11:01:04 PM
Last modification on : Wednesday, December 9, 2020 - 3:12:54 AM
Long-term archiving on: : Friday, June 25, 2010 - 11:24:51 AM

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  • HAL Id : hal-00466832, version 1
  • ARXIV : 1003.5059

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O. El-Fallah, K. Kellay, M. Shabankhah, H. Youssfi. Level sets and Composition operators on the Dirichlet space. Journal of Functional Analysis, Elsevier, 2011, 260 ((6)), pp.1721-1733. ⟨hal-00466832⟩

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