Geodesic
Isometric composition operators on weighted Dirichlet space
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 27-34

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We investigate isometric composition operators on the weighted Dirichlet space $\mathcal {D}_\alpha $ with standard weights $(1-|z|^2)^\alpha $, $\alpha >-1$. The main technique used comes from Martín and Vukotić who completely characterized the isometric composition operators on the classical Dirichlet space $\mathcal {D}$. We solve some of these but not in general. We also investigate the situation when $\mathcal {D}_\alpha $ is equipped with another equivalent norm.
DOI : 10.1007/s10587-016-0235-4
Classification : 46B04, 47B33, 47B38
Keywords: composition operator; weighted Dirichlet space; isometry 
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Han, Shi-An; Zhou, Ze-Hua. Isometric composition operators on weighted Dirichlet space. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 27-34. doi: 10.1007/s10587-016-0235-4

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