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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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