Advertisement

Archiv der Mathematik

, Volume 105, Issue 5, pp 453–459 | Cite as

On trace ideal weighted composition operators on weighted Fock spaces

  • Tesfa Mengestie
Article

Abstract

We recently described the Schatten \({\mathcal{S}_{p}}\) class membership of weighted composition operators on Fock–Sobolev spaces and a large class of weighted Fock spaces, where the weights defining such spaces are radial and satisfy a certain mild smoothness condition, in terms of a simple L p integrability condition whenever p ≥ 2. We continue that line of research to extend and complete the gap when 0 <  p <  2.

Keywords

Fock–Sobolev spaces Weighted Fock spaces Weighted composition operator Schatten class membership 

Mathematics Subject Classification

31B05 39A12 31C20 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cho H. R., Choe B. R., Koo H.: Linear combinations of composition operators on the Fock–Sobolev spaces, Potential Analysis 4(41), 1223–1246 (2014)MathSciNetCrossRefGoogle Scholar
  2. 2.
    R. Cho and K. Zhu, Fock–Sobolev spaces and their Carleson measures, Journal of Functional Analysis Volume, 263, Issue 8, 15 (2012), 2483–2506.Google Scholar
  3. 3.
    Mengestie T.: Carleson type measures for Fock–Sobolev spaces, Complex Analysis and Operator Theory 8, 1225–1256 (2014)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Mengestie T.: Schatten class weighted composition operators on weighted Fock spaces, Arch. Math. 101, 349–360 (2013)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Seip K., Youssfi El.: Hankel operators on Fock spaces and related Bergman kernel estimates, Journal of Geometric Analysis 23, 170–201 (2013)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    K. Zhu, Operator theory in function spaces, Mathematical Surveys and Monographs, Vol 138. Amer. Math. Soc., Providence, RI., 2007.Google Scholar

Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of Mathematical SciencesStord/Haugesund University College (HSH)StordNorway

Personalised recommendations