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Paracommutators—boundedness and Schatten-von Neumann properties

Authors: Svante Janson and Jaak Peetre
Journal: Trans. Amer. Math. Soc. 305 (1988), 467-504
MSC: Primary 47B38; Secondary 42B20, 47B10, 47B35
MathSciNet review: 924766
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Abstract: A very general class of operators, acting on functions in ${L^2}({{\mathbf {R}}^d})$, is introduced. The name "paracommutator" has been chosen because of the similarity with the paramultiplication of Bony and also because paracommutators comprise as a special case commutators of Calderón-Zygmund operators, as well as many other interesting examples (Hankel and Toeplitz operators etc.). The main results, extending previous results by Peller and others, express boundedness and Schatten-von Neumann properties of a paracommutator in terms of its symbol.

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