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Orthogonal polynomials and middle Hankel operators on Bergman spaces

Lizhong Peng; Richard Rochberg; Zhijian Wu — 1992

Studia Mathematica

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.

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