Harmonic Analysis and Applications

June 4-8, 2018


"Boundedness results for pseudodifferential operators"

D'Elia, Lorenza

The analysis of boundedness results for Weyl operators and \tau-operators has been pursed by many authors. We study these operators from a time-frequency perspective, using the relative time-frequency representations. We provide sufficient conditions for the boundedness of these operators acting on modulation spaces and having symbols in weighted Wiener amalgam spaces. In the case of \tau-operator, we exibit a function of parameter \tau which is an upper bound for the operator norm. It is well known the continuity properties of \tau-operators on modulation space when the symbol belongs to modulation space as well. In this context, we find an upper bound for the operator norm which does not depend on the parameter, as expected. Key ingredients are uniform continuity estimates for the \tau- Wigner distributions.

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