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Trace ideal criteria for Toeplitz and Hankel operators on the weighted Bergman spaces with exponential type weights. (English) Zbl 0853.47015
Let $\varphi: \bbfD\to \bbfR$ be a subharmonic function and let $AL^2_\varphi(\bbfD)$ denote the closed subspace of $L^2(\bbfD, e^{- 2\varphi} dA)$ consisting of analytic functions in the unit disk $\bbfD$. For a certain class of subharmonic $\varphi$, the necessary and sufficient conditions are obtained for the Toeplitz operator $T_\mu$ on $AL^2_\varphi(\bbfD)$ and the Hankel operator $H_b$ on $AL^2_\varphi(\bbfD)$ in order that they belong to the Schatten-von Neumann class $S_p$.
Reviewer: P.Lin (St.Louis)

47B35Toeplitz operators, Hankel operators, Wiener-Hopf operators
47B10Operators belonging to operator ideals
46J15Banach algebras of differentiable or analytic functions, $H^p$-spaces