Publications
Journal Articles
2.
Cordero, Elena; D'Elia, Lorenza; Trapasso, S. Ivan
Norm estimates for τ-pseudodifferential operators in Wiener amalgam and modulation spaces Journal Article
In: J. Math. Anal. Appl., vol. 471, no. 1-2, pp. 541–563, 2019.
Abstract | Links | BibTeX | Tags: harmonic analysis, modulation spaces, pseudodifferential operators, time-frequency analysis, Wiener amalgam spaces
@article{CDT_JMAA_19,
title = {Norm estimates for τ-pseudodifferential operators in Wiener amalgam and modulation spaces},
author = {Elena Cordero and Lorenza D'Elia and S. Ivan Trapasso},
url = {https://arxiv.org/abs/1803.07865, arXiv
https://www.sciencedirect.com/science/article/pii/S0022247X18309193/pdfft?md5=56e69bc9745c316f260d37420041913d&pid=1-s2.0-S0022247X18309193-main.pdf, PDF},
doi = {10.1016/j.jmaa.2018.10.090},
year = {2019},
date = {2019-03-01},
urldate = {2019-03-01},
journal = {J. Math. Anal. Appl.},
volume = {471},
number = {1-2},
pages = {541–563},
publisher = {Academic Press},
abstract = {We study continuity properties on modulation spaces for (tau)-pseudodifferential operators with symbols (a) in Wiener amalgam spaces. We obtain boundedness results for (tau in (0,1)) whereas, in the end-points (tau=0) and (tau=1), the corresponding operators are in general unbounded. Furthermore, for (tau in (0,1)), we exhibit a function of (tau) which is an upper bound for the operator norm.
The continuity properties of (tau)-pseudodifferential operators, for any (tauin [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 in [0,1]), as expected. Key ingredients are uniform continuity estimates for (tau)-Wigner distributions.},
keywords = {harmonic analysis, modulation spaces, pseudodifferential operators, time-frequency analysis, Wiener amalgam spaces},
pubstate = {published},
tppubtype = {article}
}
We study continuity properties on modulation spaces for \(\tau\)-pseudodifferential operators with symbols \(a\) in Wiener amalgam spaces. We obtain boundedness results for \(\tau \in (0,1)\) whereas, in the end-points \(\tau=0\) and \(\tau=1\), the corresponding operators are in general unbounded. Furthermore, for \(\tau \in (0,1)\), we exhibit a function of \(\tau\) which is an upper bound for the operator norm.
The continuity properties of \(\tau\)-pseudodifferential operators, for any \(\tau\in [0,1]\), 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 \(\tau \in [0,1]\), as expected. Key ingredients are uniform continuity estimates for \(\tau\)-Wigner distributions.
The continuity properties of \(\tau\)-pseudodifferential operators, for any \(\tau\in [0,1]\), 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 \(\tau \in [0,1]\), as expected. Key ingredients are uniform continuity estimates for \(\tau\)-Wigner distributions.
1.
D'Elia, Lorenza; Trapasso, S. Ivan
Boundedness of pseudodifferential operators with symbols in Wiener amalgam spaces on modulation spaces Journal Article
In: J. Pseudo-Differ. Oper. Appl., vol. 9, pp. 881–890, 2018.
Abstract | Links | BibTeX | Tags: harmonic analysis, modulation spaces, pseudodifferential operators, time-frequency analysis, Wiener amalgam spaces
@article{DT_JPDO_18,
title = {Boundedness of pseudodifferential operators with symbols in Wiener amalgam spaces on modulation spaces},
author = {Lorenza D'Elia and S. Ivan Trapasso},
url = {https://arxiv.org/abs/1703.08989, arXiv},
doi = {10.1007/s11868-017-0220-1},
year = {2018},
date = {2018-12-01},
urldate = {2018-12-01},
journal = {J. Pseudo-Differ. Oper. Appl.},
volume = {9},
pages = {881–890},
publisher = {Springer International Publishing},
abstract = {This paper provides sufficient conditions for the boundedness of Weyl operators on modulation spaces. The Weyl symbols belong to Wiener amalgam spaces, or generalized modulation spaces, as recently renamed by their inventor Hans Feichtinger. This is the first result which relates symbols in Wiener amalgam spaces to operators acting on classical modulation spaces.},
keywords = {harmonic analysis, modulation spaces, pseudodifferential operators, time-frequency analysis, Wiener amalgam spaces},
pubstate = {published},
tppubtype = {article}
}
This paper provides sufficient conditions for the boundedness of Weyl operators on modulation spaces. The Weyl symbols belong to Wiener amalgam spaces, or generalized modulation spaces, as recently renamed by their inventor Hans Feichtinger. This is the first result which relates symbols in Wiener amalgam spaces to operators acting on classical modulation spaces.