충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제26권3호
  • /
  • Pages.467-475
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  • 2013
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  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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BOUNDEDNESS AND COMPACTNESS OF SOME TOEPLITZ OPERATORS

  • Kang, Si Ho (Department of Mathematics Sookmyung Women's University)
  • 투고 : 2013.03.08
  • 심사 : 2013.07.08
  • 발행 : 2013.08.15
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초록

We consider the problem to determine when a Toeplitz operator is bounded on weighted Bergman spaces. We introduce some set CG of symbols and we prove that Toeplitz operators induced by elements of CG are bounded and characterize when Toeplitz operators are compact and show that each element of CG is related with a Carleson measure.

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과제정보

연구 과제 주관 기관 : Sookmyung Women's University

참고문헌

  1. S. Axler, The Bergman Space the Bloch space and commutators of multiplication operators, Duke Math. J. 53 (1986), no. 2, 315-332. https://doi.org/10.1215/S0012-7094-86-05320-2
  2. S. Axler and D. Zheng, Compact operators via the Berezin transform, Indiana Univ. Math. 47 (1998), 387-399.
  3. A. Brown, P. R. Halmos, and A. L. Shields, Cesaro operators, Acta Sci. Math. (Szeged) 26 (1965), 125-137.
  4. K. Stroethoff, Compact Toeplitz operators on the Bergman space, Math. Proc. Cambridge Philos. Soc. 124 (1998), no. 1, 151-160. https://doi.org/10.1017/S0305004197002375
  5. K. Zhu, Operator theory in function spaces, Marcell-Dekker, Inc., New york, 1990.