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.

Norm estimates for τ-pseudodifferential operators in Wiener amalgam and modulation spaces / Trapasso, salvatore ivan; Cordero, Elena; D'Elia, Lorenza. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 471:1-2(2019), pp. 541-563. [10.1016/j.jmaa.2018.10.090]

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

trapasso, salvatore ivan;
2019

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2971948