Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

LIPSCHITZ CONTINUOUS AND COMPACT COMPOSITION OPERATOR ACTING BETWEEN SOME WEIGHTED GENERAL HYPERBOLIC-TYPE CLASSES

  • Kamal, A. (Department of Mathematics Port Said University) ;
  • El-Sayed Ahmed, A. (Mathematics Department Sohag University) ;
  • Yassen, T.I. (Department of Mathematics Port Said University)
  • Received : 2016.03.14
  • Accepted : 2016.12.07
  • Published : 2016.12.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we study Lipschitz continuous, the boundedness and compactness of the composition operator $C_{\phi}$ acting between the general hyperbolic Bloch type-classes ${\mathcal{B}}^{\ast}_{p,{\log},{\alpha}}$ and general hyperbolic Besov-type classes $F^{\ast}_{p,{\log}}(p,q,s)$. Moreover, these classes are shown to be complete metric spaces with respect to the corresponding metrics.

Keywords

References

  1. A. El-Sayed Ahmed and M. A. Bakhit, Composition operators on some holomorphic Banach function spaces, Math. Scand. 104 (2) (2009), 275-295. https://doi.org/10.7146/math.scand.a-15098
  2. A. El-Sayed Ahmed and M. A. Bakhit, Composition operators acting between some weighted Mobius invariant spaces, Ann. Funct. Anal. AFA 2 (2) (2011), 138-152 https://doi.org/10.15352/afa/1399900202
  3. A. El-Sayed Ahmed, Natural metrics and composition operators in generalized hyperbolic function spaces, J. Inequal. Appl. 185 (2012), 1-13.
  4. S. Charpentier, Compact composition operators on the Hardy-Orlicz and weighted Bergman-Orlicz spaces on the ball, J. Oper. Theory 69 (2) (2013), 463-481. https://doi.org/10.7900/jot.2011jan23.1913
  5. M. Kotilainen, Studies on composition operators and function spaces, Report Series. Department of Mathematics, University of Joensuu 11. Joensuu. (Dissertation) (2007).
  6. L. Luo and J. Chen, Essential norms of composition operators between weighted Bergman spaces of the unit disc, Acta Math. Sin., Engl. Ser. 29 (4) (2013), 633-638. https://doi.org/10.1007/s10114-012-0070-y
  7. S. Makhmutov and M. Tjani, Composition operators on some Mobius invariant Banach spaces, Bull. Austral. Math. Soc. 62 (2000), 1-19. https://doi.org/10.1017/S0004972700018426
  8. X. Li, F. Perez-Gonzalez and J. Rattya, Composition operators in hyperbolic Q-classes, Ann. Acad. Sci. Fenn. Math. 31 (2006), 391-404.
  9. F. Perez-Gonzalez, J.Rattya and J. Taskinen, Lipschitz continuous and compact composition operators in hyperbolic classes, Mediterr. J. Math. 8 (2011), 123-135. https://doi.org/10.1007/s00009-010-0054-z
  10. K. Stroethoff, Besov-type characterizations for the Bloch space, Bull. Austral. Math. Soc. 39 (1989), 405-420. https://doi.org/10.1017/S0004972700003324
  11. M. Tjani, Compact composition operators on Besov spaces, Trans. Amer. Math. Soc. 355 (2003), 4683-4698. https://doi.org/10.1090/S0002-9947-03-03354-3
  12. J. Zhou, Composition operators from ${\mathcal{B}}^{\alpha}$ to ${\mathcal{Q}}_K$ type spaces, J. Funct. Spaces Appl. 6 (1) (2008), 89-105.

Cited by

  1. Certain Classes of Operators on Some Weighted Hyperbolic Function Spaces vol.2021, pp.None, 2016, https://doi.org/10.1155/2021/6664398
  2. Refinements on Some Classes of Complex Function Spaces vol.13, pp.2, 2021, https://doi.org/10.3390/sym13020339