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

We study continuity properties on modulation spaces for tau-pseudodifferential operators Op(tau) (a) with symbols a in Wiener amalgam spaces. We obtain boundedness results for tau is an element of(0, 1) whereas, in the end-points tau = 0 and tau = 1, the corresponding operators are in general unbounded. Furthermore, for tau is an element of(0, 1), we exhibit a function of tau which is an upper bound for the operator norm. The continuity properties of Op(tau) (a), for any tau is an element of[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 tau is an element of[0, 1], as expected. Key ingredients are uniform continuity estimates for tau-Wigner distributions. (C) 2018 Elsevier Inc. All rights reserved.