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Some Toeplitz operators on weighted Bergman spaces

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대한수학회 (The Korean Mathematical Society)|2011.01|대한수학회보 (Bulletin of the KMS)|제48권 제1호|pp. 141-149

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참고문헌

키워드

Toeplitz operatorsweighted Bergman spacesintegral operatorsBerezin transforms
주제분류수학

초록

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

Abstract

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

참고문헌 (5)

  1. S. Axler, "The Bergman space, the Bloch space, and commutators of multiplication oper-ators", Duke Math. J, 53(2), pp.315~332 (1986)
  2. S. Axler, "Compact operators via the Berezin Transform", Indiana Univ. Math, 47, pp.387~399 (1988)
  3. A. Brown, "Cesaro operators", Acta Sci. Math. (Szeged), 26, pp.125~137 (1965)
  4. K. Stroethoff, "Compact Toeplitz operators on Bergman spaces", Math. Proc. Cambridge Philos. Soc, 124(1), pp.151~160 (1998)
  5. K. Zhu, "Operator Theory in Function Spaces" (1990), Marcel Dekker, Inc

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