Lobachevskii Journal of Mathematics

, Volume 39, Issue 2, pp 179–184 | Cite as

Operators on Weighted Lorentz–Karamata–Bochner Spaces

Article
  • 7 Downloads

Abstract

In this paper, conditions are derived for the multiplication, composition and weighted composition operators on weighted Lorentz–Karamata–Bochner (WLKB) spaces L p,q,w;b , 1 < p ≤ ∞, 1 ≤ q ≤ ∞, to be bounded.

Keywords and phrases

Lorentz–Karamata–Bochner space multiplication operators composition operator compact operator distribution function slowly varying function 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. C. Arora, G. Datt, and S. Verma, “Composition operators on Lorentz spaces,” Bull. Aust.Math. Soc. 76, 205–214 (2007).MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    S. C. Arora, G. Datt, and S. Verma, “Weighted composition operators on Lorentz spaces,” Bull. Korean. Math. Soc. 44, 701–708 (2007).MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    S. C. Arora, G. Datt, and S. Verma, “Multiplication and composition operators on Lorentz–Bochner spaces,” Osaka J.Math. 45, 629–641 (2008).MathSciNetMATHGoogle Scholar
  4. 4.
    O. Blasco and J. V. Neerven, “Space of operator-valued functions measurable with respect to the strong operator topology,” arXiv:o811.2284v2[math.FA] (2009).Google Scholar
  5. 5.
    G. Datt and S. C. Arora, “Injective composition operators on Lorentz–Bochner spaces,” Demonstr. Math. 46, 741–756 (2013).MathSciNetMATHGoogle Scholar
  6. 6.
    G. Datt, R. Chugh, and J. Jakhar, “A note on multiplication operators between Lorentz–Karamata spaces,” Brit. J. Math. Comput. Sci. 11 (2), 1–10 (2015).CrossRefGoogle Scholar
  7. 7.
    G. Datt, R. Chugh, and J. Jakhar, “Weighted composition operators induced by strongly measurable functions” (Communicated).Google Scholar
  8. 8.
    D. E. Edmunds and W. D. Evans, Hardy Operators, Function Spaces and Embeddings, Springer Monographs inMathematics (Springer, Berlin, 2004).CrossRefGoogle Scholar
  9. 9.
    I. Eryilmaz, “Weighted composition operators on weighted Lorentz–Karamata spaces,” Stud. Univ. Babes- Bolyai Math. 57, 111–119 (2012).MathSciNetMATHGoogle Scholar
  10. 10.
    I. Eryilmaz, “Multiplication operators on Lorentz–Karamata–Bochner spaces,” Math. Slov. 62, 293–300 (2012).MathSciNetMATHGoogle Scholar
  11. 11.
    A. Gupta and P. Sharma, “Weighted composition operators on Lorentz–Karamata–Bochner spaces,” J. Adv. Res. Pure Math. 7 (2), 76–88 (2015).MathSciNetGoogle Scholar
  12. 12.
    R. K. Singh and J. S. Manhas, Composition Operators on Function Spaces, Vol. 179 of North-Holland Mathematics Studies (North-Holland, Amsterdam, 1993).MATHGoogle Scholar
  13. 13.
    H. Takagi and K. Yokouchi, “Multiplication and composition operators between two L p spaces,” Contemp. Math. 232, 321–338 (1999).CrossRefMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Department of Mathematics, PGDAV CollegeUniversity of DelhiDelhiIndia
  2. 2.Department of MathematicsM.D. UniversityRohtak, HaryanaIndia

Personalised recommendations