Orthogonal polynomials and middle Hankel operators on Bergman spaces

Volume 102 / 1992

Lizhong Peng, , Studia Mathematica 102 (1992), 57-75 DOI: 10.4064/sm-102-1-57-75


We introduce a sequence of Hankel style operators $H^k$, k = 1,2,3,..., which act on the Bergman space of the unit disk. These operators are intermediate between the classical big and small Hankel operators. We study the boundedness and Schatten-von Neumann properties of the $H^k$ and show, among other things, that $H^k$ are cut-off at 1/k. Recall that the big Hankel operator is cut-off at 1 and the small Hankel operator at 0.


  • Lizhong Peng

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