On bounded pseudodifferential operators in a high-dimensional setting

L. Amour 1 L. Jager J. Nourrigat 2
1 CIR
LISSI - Laboratoire Images, Signaux et Systèmes Intelligents
Abstract : This work is concerned with extending the results of Calderón and Vaillancourt proving the boundedness of Weyl pseudodifferential operators Op W eyl h (F) in L 2 (R n). We state conditions under which the norm of such operators has an upper bound independent of n. To this aim, we apply a decomposition of the identity to the symbol F , thus obtaining a sum of operators of a hybrid type, each of them behaving as a Weyl operator with respect to some of the variables and as an anti-Wick operator with respect to the other ones. Then we establish upper bounds for these auxiliary operators, using suitably adapted classical methods like coherent states.
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L. Amour, L. Jager, J. Nourrigat. On bounded pseudodifferential operators in a high-dimensional setting. Proceedings of the American Mathematical Society, American Mathematical Society, 2015, 143 (5), pp.2057 - 2068. ⟨10.1090/S0002-9939-2014-12379-3⟩. ⟨hal-01881704⟩

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