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On the boundedness and compactness of operators of Hankel type. (English) Zbl 0793.47022
The authors obtain boundedness and compactness criteria for commutators of the multiplication by a function $$f$$ operator with a general class of integral operators having kernels of a critical homogeneity and which are modeled after the Bergman projection.
It is shown that the commutator is bounded or compact on $$L^ p$$ whenever the function $$f$$ is an appropriately defined BMO or VMO space, respectively. As an application the commutators with the Bergman projection in strictly pseudoconvex domains in $$\mathbb{C}^ n$$ and finite type domains in $$\mathbb{C}^ 2$$ are considered.

##### MSC:
 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 46J15 Banach algebras of differentiable or analytic functions, $$H^p$$-spaces 32T99 Pseudoconvex domains 32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
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