On bounded pseudodifferential operators in a high-dimensional setting
Abstract
This work is concerned with extending the results of Calder\' on and Vaillancourt proving the boundedness of Weyl pseudo differential operators Op_h^{weyl} (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.
Cite
@article{arxiv.1303.1972,
title = {On bounded pseudodifferential operators in a high-dimensional setting},
author = {Laurent Amour and Lisette Jager and Jean Nourrigat},
journal= {arXiv preprint arXiv:1303.1972},
year = {2014}
}
Comments
This result is a consequence of a former paper (arXiv 1209:2852) but it is convenient to have a statement and a proof which do not require infinite dimensional spaces