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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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Paracommutators—boundedness and Schatten-von Neumann properties
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by Svante Janson and Jaak Peetre PDF
Trans. Amer. Math. Soc. 305 (1988), 467-504 Request permission

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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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 305 (1988), 467-504
  • MSC: Primary 47B38; Secondary 42B20, 47B10, 47B35
  • DOI: https://doi.org/10.1090/S0002-9947-1988-0924766-6
  • MathSciNet review: 924766