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Generalized Cesàro operators on Dirichlet-type spaces

Abstract

In this note, we introduce and study a new kind of generalized Cesàro operator, \(\cal{C}_{\mu}\), induced by a positive Borel measure μ on [0, 1) between Dirichlet-type spaces. We characterize the measures μ for which \(\cal{C}_{\mu}\) is bounded (compact) from one Dirichlet-type space, \(\cal{D}_{\alpha}\), into another one, \(\cal{D}_{\beta}\).

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Corresponding authors

Correspondence to Jianjun Jin or Shuan Tang.

Additional information

The first author was supported by National Natural Science Foundation of China (11501157). The second author was supported by National Natural Science Foundation of China (12061022) and the foundation of Guizhou Provincial Science and Technology Department ([2017]7337 and [2017]5726).

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Jin, J., Tang, S. Generalized Cesàro operators on Dirichlet-type spaces. Acta Math Sci 42, 212–220 (2022). https://doi.org/10.1007/s10473-022-0111-2

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  • DOI: https://doi.org/10.1007/s10473-022-0111-2

Key words

  • generalized Cesàro operator
  • Dirichlet-type spaces
  • Carleson measure
  • boundedness and compactness of operator

2010 MR Subject Classification

  • 47B38
  • 31C25