Boundedness and compactness of weighted composition operators between weighted Bergman spaces

Elke Wolf

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2012)

  • Volume: 66, Issue: 1
  • ISSN: 0365-1029

Abstract

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We study when a weighted composition operator acting between different weighted Bergman spaces is bounded, resp. compact.

How to cite

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Elke Wolf. "Boundedness and compactness of weighted composition operators between weighted Bergman spaces." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 66.1 (2012): null. <http://eudml.org/doc/289792>.

@article{ElkeWolf2012,
abstract = {We study when a weighted composition operator acting between different weighted Bergman spaces is bounded, resp. compact.},
author = {Elke Wolf},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Weighted Bergman space; composition operator},
language = {eng},
number = {1},
pages = {null},
title = {Boundedness and compactness of weighted composition operators between weighted Bergman spaces},
url = {http://eudml.org/doc/289792},
volume = {66},
year = {2012},
}

TY - JOUR
AU - Elke Wolf
TI - Boundedness and compactness of weighted composition operators between weighted Bergman spaces
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2012
VL - 66
IS - 1
SP - null
AB - We study when a weighted composition operator acting between different weighted Bergman spaces is bounded, resp. compact.
LA - eng
KW - Weighted Bergman space; composition operator
UR - http://eudml.org/doc/289792
ER -

References

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  4. Contreras, M. D., Hernandez-Dıaz, A. G., Weighted composition operators in weighted Banach spaces of analytic functions, J. Austral. Math. Soc. Ser. A 69 (2000), no. 1, 41-60. 
  5. Cowen, C., MacCluer, B., Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995. 
  6. Cuckovic, Z., Zhao, R., Weighted composition operators on the Bergman space, J. London Math. Soc. (2) 70 (2004), no. 2, 499-511. 
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  9. Hedenmalm, H., Korenblum, B. and Zhu, K., Theory of Bergman spaces, Graduate Texts in Mathematics, 199, Springer–Verlag, New York, 2000. 
  10. Kriete, T., MacCluer, B., Composition operators on large weighted Bergman spaces, Indiana Univ. Math. J. 41 (1992), no. 3, 755-788. 
  11. Moorhouse, J., Compact differences of composition operators, J. Funct. Anal. 219 (2005), no. 1, 70-92. 
  12. MacCluer, B., Ohno, S. and Zhao, R., Topological structure of the space of composition operators on H , Integral Equations Operator Theory 40 (2001), no. 4, 481-494. 
  13. Nieminen, P., Compact differences of composition operators on Bloch and Lipschitz spaces, Comput. Methods Funct. Theory 7 (2007), no. 2, 325-344. 
  14. Palmberg, N., Weighted composition operators with closed range, Bull. Austral. Math. Soc. 75 (2007), no. 3, 331-354. 
  15. Shapiro, J. H., Composition Operators and Classical Function Theory, Universitext: Tracts in Mathematics. Springer-Verlag, New York, 1993. 
  16. Wolf, E., Weighted composition operators between weighted Bergman spaces, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Math. RACSAM 103 (2009), no. 1, 11-15. 

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