Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

A NOTE OF WEIGHTED COMPOSITION OPERATORS ON BLOCH-TYPE SPACES

  • LI, SONGXIAO (INSTITUTE OF SYSTEM ENGINEERING MACAU UNIVERSITY OF SCIENCE AND TECHNOLOGY) ;
  • ZHOU, JIZHEN (SCHOOL OF SCIENCE ANHUI UNIVERSITY OF SCIENCE AND TECHNOLOGY)
  • Received : 2014.11.19
  • Published : 2015.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

We obtain a new criterion for the boundedness and compactness of the weighted composition operators ${\psi}C_{\varphi}$ from ${\ss}^{{\alpha}}$(0 < ${\alpha}$ < 1) to ${\ss}^{{\beta}}$ in terms of the sequence $\{{\psi}{\varphi}^n\}$. An estimate for the essential norm of ${\psi}C_{\varphi}$ is also given.

Keywords

References

  1. J. Anderson, J. Clunie, and Ch. Pommerenke, On Bloch functions and normal functions, J. Reine Angew. Math. 270 (1974), 12-37.
  2. M. Contreras and A. Hernandez-Diaz, Weighted composition operators in weighted Banach spaces of analytic functions, J. Austral. Math. Soc. Ser. A 69 (2000), no. 1, 41-60. https://doi.org/10.1017/S144678870000183X
  3. C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, 1995.
  4. S. Li and S. Stevic, Weighted composition operators from Bergman-type spaces into Bloch spaces, Proc. Indian Acad. Sci. Math. Sci. 117 (2007), no. 3, 371-385. https://doi.org/10.1007/s12044-007-0032-y
  5. Z. Lou, Composition operators on Bloch type spaces, Analysis 23 (2003), no. 1, 81-95.
  6. B. Maccluer and R. Zhao, Essential norm of weighted composition operators between Bloch-type spaces, Rocky Mountain J. Math. 33 (2003), no. 4, 1437-1458. https://doi.org/10.1216/rmjm/1181075473
  7. K. Madigan and A. Matheson, Compact composition operators on the Bloch space, Trans. Amer. Math. Soc. 347 (1995), no. 7, 2679-2687. https://doi.org/10.1090/S0002-9947-1995-1273508-X
  8. J. Manhas and R. Zhao, New estimates of essential norms of weighted composition operators between Bloch type spaces, J. Math. Anal. Appl. 389 (2012), no. 1, 32-47. https://doi.org/10.1016/j.jmaa.2011.11.039
  9. A. Montes-Rodriguez, Weighted composition operators on weighted Banach spaces of analytic functions, J. London Math. Soc. 61 (2000), no. 3, 872-884. https://doi.org/10.1112/S0024610700008875
  10. S. Ohno, K. Stroethoff, and R. Zhao, Weighted composition operators between Bloch-type spaces, Rocky Mountain J. Math. 33 (2003), no. 1, 191-215. https://doi.org/10.1216/rmjm/1181069993
  11. S. Ohno and R. Zhao, Weighted composition operators on the Bloch space, Bull. Austral. Math. Soc. 63 (2001), no. 2, 177-185. https://doi.org/10.1017/S0004972700019250
  12. S. Stevic and R. Agarwal, Weighted composition operators from logarithmic Bloch-type spaces to Bloch-type spaces, J. Inequal. Appl. 2009 (2009), Art. ID 964814, 21 pp.
  13. H. Wulan, D. Zheng, and K. Zhu, Compact composition operators on BMOA and the Bloch space, Proc. Amer. Math. Soc. 137 (2009), no. 11, 3861-3868. https://doi.org/10.1090/S0002-9939-09-09961-4
  14. R. Zhao, Essential norms of composition operators between Bloch type spaces, Proc. Amer. Math. Soc. 138 (2010), no. 7, 2537-2546. https://doi.org/10.1090/S0002-9939-10-10285-8
  15. K. Zhu, Bloch type spaces of analytic functions, Rocky Mountain J. Math. 23 (1993), no. 3, 1143-1177. https://doi.org/10.1216/rmjm/1181072549
  16. K. Zhu, Operator Theory in Function Spaces, Second edition, American Mathematical Society, Providence, 2007.