Beatrous, Frank; Li, Song-Ying On the boundedness and compactness of operators of Hankel type. (English) Zbl 0793.47022 J. Funct. Anal. 111, No. 2, 350-379 (1993). 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. Reviewer: N.L.Vasilevskij (Mexico) Cited in 1 ReviewCited in 40 Documents 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)) Keywords:boundedness; compactness; commutators of multiplication by a function; integral operators; kernels of critical homogeneity; Bergman projection in strictly pseudoconvex domains PDFBibTeX XMLCite \textit{F. Beatrous} and \textit{S.-Y. Li}, J. Funct. Anal. 111, No. 2, 350--379 (1993; Zbl 0793.47022) Full Text: DOI