Orthogonal polynomials and middle Hankel operators on Bergman spaces

Lizhong Peng; Richard Rochberg; Zhijian Wu

Studia Mathematica (1992)

  • Volume: 102, Issue: 1, page 57-75
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Peng, Lizhong, Rochberg, Richard, and Wu, Zhijian. "Orthogonal polynomials and middle Hankel operators on Bergman spaces." Studia Mathematica 102.1 (1992): 57-75. <http://eudml.org/doc/215914>.

@article{Peng1992,
abstract = {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.},
author = {Peng, Lizhong, Rochberg, Richard, Wu, Zhijian},
journal = {Studia Mathematica},
language = {eng},
number = {1},
pages = {57-75},
title = {Orthogonal polynomials and middle Hankel operators on Bergman spaces},
url = {http://eudml.org/doc/215914},
volume = {102},
year = {1992},
}

TY - JOUR
AU - Peng, Lizhong
AU - Rochberg, Richard
AU - Wu, Zhijian
TI - Orthogonal polynomials and middle Hankel operators on Bergman spaces
JO - Studia Mathematica
PY - 1992
VL - 102
IS - 1
SP - 57
EP - 75
AB - 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.
LA - eng
UR - http://eudml.org/doc/215914
ER -

References

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