[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2014.27.3.439

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

Kang, Si Ho (Department of Mathematics Sookmyung Women's University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.27, no.3, 2014 , pp. 439-454 More about this Journal

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

weighted Bergman spaces; Toeplitz operators; Bloch-type spaces; compact operators;

Citations & Related Records

Reference

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