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On the Hörmander classes of bilinear pseudodifferential operators. (English) Zbl 1213.47053
The authors introduce and study bilinear pseudodifferential operators with symbols in the bilinear analog of all the Hörmander classes. The possibility of symbolic calculus in these classes is investigated. Only some particular cases of the above classes have been used before; [see Á. Bényi and R. H. Torres, Commun. Partial Differ. Equations 28, No. 5-6, 1161–1181 (2003; Zbl 1103.35370)]. Now it becomes possible to use the symbolic calculus (when it exists) as an alternative way to recover the boundedness on products of Lebesgue spaces for the classes corresponding to operators with bilinear Calderón-Zygmund kernels. Some estimates in the form of the Leibniz rule are also given.
MSC:
47G30Pseudodifferential operators
35S05General theory of pseudodifferential operators
42B15Multipliers, several variables
42B20Singular and oscillatory integrals, several variables
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