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Characterizations of certain classes of Hankel operators on the Bergman spaces of the unit disk. (English) Zbl 0773.47014
The integrable functions on the unit disk $f$ for which the Hankel operator $H\sb f(g)=fg-P(fg)$ may be extended to a bounded operator from the Bergman space $A\sp p$ to $L\sp p$ are characterized, for $1<p<\infty$. Also characterized are those functions $f$ for which $H\sb f$ extends to a compact or Schatten class operator on $A\sp 2$.

MSC:
47B35Toeplitz operators, Hankel operators, Wiener-Hopf operators
46J15Banach algebras of differentiable or analytic functions, $H^p$-spaces
47B38Operators on function spaces (general)
47B10Operators belonging to operator ideals
47B07Operators defined by compactness properties
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References:
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