Norm Estimates for $τ$-Pseudodifferential Operators in Wiener Amalgam and Modulation Spaces

Elena Cordero; Lorenza D'Elia; Salvatore Ivan Trapasso

doi:10.1016/j.jmaa.2018.10.090

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arXiv · 1803.07865

Norm Estimates for $τ$-Pseudodifferential Operators in Wiener Amalgam and Modulation Spaces

Elena Cordero·Lorenza D'Elia·Salvatore Ivan Trapasso

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Abstract

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

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Elena Cordero, Lorenza D'Elia, Salvatore Ivan Trapasso. 2018-03-21. Norm Estimates for $τ$-Pseudodifferential Operators in Wiener Amalgam and Modulation Spaces. https://doi.org/10.1016/j.jmaa.2018.10.090

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