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A note on composition operators on certain weighted Hardy spaces

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Abstract

We study the composition operators on certain weighted Hilbert spaces \({\mathcal {H}} _\omega\), consisting of analytic functions defined on \({\mathbb {D}}\), that can be described as a weighted Dirichlet space with weight \(\omega\) having certain properties. We will use the notion of vanishing \(\omega\)-Carleson measure to characterize the compact composition operators on \({\mathcal {H}} _\omega\). Also, we give some upper and lower estimates for the essential norm of these operators and investigate the Hilbert-Schmidt composition operators.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Iran

    H. Keshavarzi & B. Khani-Robati

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  1. H. Keshavarzi
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  2. B. Khani-Robati
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Correspondence to B. Khani-Robati.

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Keshavarzi, H., Khani-Robati, B. A note on composition operators on certain weighted Hardy spaces. Rend. Circ. Mat. Palermo, II. Ser 72, 1483–1495 (2023). https://doi.org/10.1007/s12215-022-00732-z

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  • DOI: https://doi.org/10.1007/s12215-022-00732-z

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