Isometric composition operators on weighted Dirichlet space

Shi-An Han; Ze-Hua Zhou

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 1, page 27-34
  • ISSN: 0011-4642

Abstract

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We investigate isometric composition operators on the weighted Dirichlet space 𝒟 α with standard weights ( 1 - | z | 2 ) α , α > - 1 . The main technique used comes from Martín and Vukotić who completely characterized the isometric composition operators on the classical Dirichlet space 𝒟 . We solve some of these but not in general. We also investigate the situation when 𝒟 α is equipped with another equivalent norm.

How to cite

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Han, Shi-An, and Zhou, Ze-Hua. "Isometric composition operators on weighted Dirichlet space." Czechoslovak Mathematical Journal 66.1 (2016): 27-34. <http://eudml.org/doc/276814>.

@article{Han2016,
abstract = {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.},
author = {Han, Shi-An, Zhou, Ze-Hua},
journal = {Czechoslovak Mathematical Journal},
keywords = {composition operator; weighted Dirichlet space; isometry},
language = {eng},
number = {1},
pages = {27-34},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Isometric composition operators on weighted Dirichlet space},
url = {http://eudml.org/doc/276814},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Han, Shi-An
AU - Zhou, Ze-Hua
TI - Isometric composition operators on weighted Dirichlet space
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 1
SP - 27
EP - 34
AB - 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.
LA - eng
KW - composition operator; weighted Dirichlet space; isometry
UR - http://eudml.org/doc/276814
ER -

References

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  7. Martín, M. J., Vukoti{ć}, D., 10.1090/S0002-9939-05-08182-7, Proc. Am. Math. Soc. 134 (2006), 1701-1705. (2006) Zbl1082.47021MR2204282DOI10.1090/S0002-9939-05-08182-7
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  9. Ryff, J. V., 10.1215/S0012-7094-66-03340-0, Duke Math. J. 33 (1966), 347-354. (1966) MR0192062DOI10.1215/S0012-7094-66-03340-0
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  11. Shapiro, J. H., Composition Operators and Classical Function Theory, Universitext: Tracts in Mathematics Springer, New York (1993). (1993) Zbl0791.30033MR1237406

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