Norm estimates for τ-pseudodifferential operators in Wiener amalgam and modulation spaces

We study continuity properties on modulation spaces for τ-pseudodifferential operators Opτ(a) with symbols a in Wiener amalgam spaces. We obtain boundedness results for τ∈(0,1) whereas, in the end-points τ=0 and τ=1, the corresponding operators are in general unbounded. Furthermore, for τ∈(0,1), we exhibit a function of τ which is an upper bound for the operator norm. The continuity properties of Opτ(a), for any τ∈[0,1], with symbols a in modulation spaces are well known. Here we find an upper bound for the operator norm which does not depend on the parameter τ∈[0,1], as expected. Key ingredients are uniform continuity estimates for τ-Wigner distributions.