"Schatten properties, nuclearity and minimality of phase shift invariant spaces"Toft, JoachimFeichtinger's minimality essentially shows that smallest non-trivial time-frequency shift invariant Banach spaces are Feichtinger algebras weighted by submulipticative weights. We extend this minimality property to the quasi-Banach case. That is, if 0<p?1 is fixed and we have a non-trivial translation and modulation invariant quasi-Banach space B of order p, then B contains, the weighted M^p space, with weight obtaining from the norm estimates under actions of the translation and modulation operators. We use these results to prove that the pseudo-differential operator with symbol in M^p is a $p$-nuclear operator from M^\infty to $M^p$. We also deduce certain Schatten-von Neumann properties for such operators when acting on modulation spaces (which do not need to be Hilbert spaces). |
| https://ps-mathematik.univie.ac.at/e/talks/strobl22_Toft_2022-06_NuclearSchatten1.pdf |
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