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TOEPLITZ OPERATORS ON BLOCH-TYPE SPACES AND A GENERALIZATION OF BLOCH-TYPE SPACES

  • Kang, Si Ho (Department of Mathematics Sookmyung Women's University)
  • Received : 2014.04.30
  • Accepted : 2014.06.30
  • Published : 2014.08.15

Abstract

We deal with the boundedness of the n-th derivatives of Bloch-type functions and Toeplitz operators and give a relationship between Bloch-type spaces and ranges of Toeplitz operators. Also we prove that the vanishing property of ${\parallel}uk^{\alpha}_z{\parallel}_{s,{\alpha}}$ on the boundary of $\mathbb{D}$ implies the compactness of Toeplitz operators and introduce a generalization of Bloch-type spaces.

Keywords

Acknowledgement

Supported by : Sookmyung women's Universety

References

  1. S. Axler and D. Zheng, Compact Operators via the Berezin Transform, Indiana Univ. Math. J. 47 (1988), 387-399.
  2. S. H. Kang, Some Toeplitz Operators on weighted Bergman Spaces, Bull. Korean. Math. Soc. 42 (2011), no. 1, 141-149.
  3. K. Stroethoff, Compact Toeplitz Operators on the Bergman Spaces, Math. Proc. Cambridge philos. Soc. 124 (1999), no. 1, 151-160.
  4. K. Zhu, Operator Theory in Function Spaces, Marcell Dekker, New York, 1990.
  5. K. Zhu, Bloch Type Spaces of Analytic Functions, Rocky Mountain Journal of Math. 23 (1993), no. 3, 1143-1177. https://doi.org/10.1216/rmjm/1181072549

Cited by

  1. BLOCH-TYPE SPACES AND THEIR COMPOSITION OPERATORS vol.37, pp.4, 2015, https://doi.org/10.5831/HMJ.2015.37.4.387