Skip to main content

Weighted Composition Operators between Mixed Norm Spaces and Spaces in the Unit Ball

Abstract

Let be an analytic self-map and let be a fixed analytic function on the open unit ball in. The boundedness and compactness of the weighted composition operator between mixed norm spaces and are studied.

[12345678910]

References

  1. Cowen CC, MacCluer BD: Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics. CRC Press, Boca Raton, Fla, USA; 1995:xii+388.

    Google Scholar 

  2. Shields AL, Williams DL: Bonded projections, duality, and multipliers in spaces of analytic functions. Transactions of the American Mathematical Society 1971, 162: 287–302.

    MathSciNet  Google Scholar 

  3. Ohno S: Weighted composition operators between and the Bloch space. Taiwanese Journal of Mathematics 2001,5(3):555–563.

    MathSciNet  MATH  Google Scholar 

  4. Li S, Stević S: Weighted composition operators between and -Bloch spaces in the unit ball. to appear in Taiwan Journal of Mathematics to appear in Taiwan Journal of Mathematics

  5. Sharma AK, Sharma SD: Weighted composition operators between Bergman-type spaces. Communications of the Korean Mathematical Society 2006,21(3):465–474.

    Article  MATH  Google Scholar 

  6. Clahane DD, Stević S: Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball. Journal of Inequalities and Applications 2006, 2006: 11 pages.

    Article  Google Scholar 

  7. Zhu X: Weighted composition operators between and Bergman type spaces. Communications of the Korean Mathematical Society 2006,21(4):719–727.

    Article  MATH  Google Scholar 

  8. Rudin W: Function Theory in the Unit Ball of n. In Fundamental Principles of Mathematical Science. Volume 241. Springer, Berlin, Germany; 1980:xiii+436.

    Google Scholar 

  9. Stević S: On generalized weighted Bergman spaces. Complex Variables 2004,49(2):109–124. 10.1080/02781070310001650047

    Article  MathSciNet  MATH  Google Scholar 

  10. Madigan K, Matheson A: Compact composition operators on the Bloch space. Transactions of the American Mathematical Society 1995,347(7):2679–2687. 10.2307/2154848

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Stevo Stević.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Stević, S. Weighted Composition Operators between Mixed Norm Spaces and Spaces in the Unit Ball. J Inequal Appl 2007, 028629 (2008). https://doi.org/10.1155/2007/28629

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/2007/28629

Keywords