Related papers: Quasi-Banach Schatten-von Neumann properties in We…

We establish continuity and Schatten-von Neumann properties for matrix operators with matrices satisfying mixed quasi-norm estimates. These considerations also include the case when the Lebesgue and Schatten parameters are allowed to stay…

Let $\Op_t(a)$, for $t\in \mathbf R$, be the pseudo-differential operator $$ f(x) \mapsto (2\pi)^{-n}\iint a((1-t)x+ty,\xi)f(y)e^{i\scal {x-y}\xi} dyd\xi $$ and let $\mathscr I_p$ be the set of Schatten-von Neumann operators of order $p\in…

Let $G$ be a compact Lie group of dimension $n.$ In this work we characterise the membership of classical pseudo-differential operators on $G$ in the trace class ideal $S_{1}(L^2(G)),$ as well as in the setting of the Schatten ideals…

We obtain a number of explicit estimates for quasi-norms of pseudo-differential operators in the Schatten-von Neumann classes $S_q$ with $0<q\le 1$. The estimates are applied to derive semi-classical bounds for operators with smooth or…

As main result, we show that a pseudodifferential operator in the Weyl calculus, whose symbol has compact Fourier support, lies in the Schatten class $\mathcal S^p$ if and only if its symbol lies in the Lebesgue space $L^p$ on phase space.…

We combine our previous results on magnetic pseudo-differential operators for H\"ormander symbols dominated by tempered weights [arXiv:2511.07184] with the magnetic Weyl super calculus of Lee and Lein [arXiv:2201.11487, arXiv:2405.19964].…

We investigate the Schatten-class properties of pseudo-differential operators with the (revisted) method of Cordes and Kato. As symbol classes we use classes similar to those of Cordes in which the $L^{\infty}$% -conditions are replaced by…

In this paper. we study properties such as $L^r$-boundedness, compactness, belonging to Schatten classes and nuclearity, Riesz spectral theory, Fredholmness, ellipticity and Gohberg's lemma, among others, for pseudo-differential operators…

We consider modulation space and spaces of Schatten-von Neumann symbols where corresponding pseudo-differential operators map one Hilbert space to another. We prove H\"older-Young and Young type results for such spaces under dilated…

We investigate the Schatten-von Neumann properties of pseudo-differential operators using the method proposed by A. Boulkhemair in \cite{Boulkhemair 2}. The symbols are elements of the ideals $S_{w}^{p}$ of the Sj\"ostrand algebra $S_{w}$.

We extend the matrix representation of magnetic pseudo-differential operators in a tight Gabor frame from [arXiv:1804.05220, arXiv:2212.12229] to asymmetrical quantizations and smooth symbols dominated by a tempered weight (and not just…

The aim of this article is to prove a Beals type characterization theorem for pseudodifferential operators in Wiener spaces. The definition of pseudodifferential operators in Wiener spaces and a Calder\'on-Vaillancourt type result appear in…

We extend Feichtinger's minimality property on smallest non-trivial time-frequency shift invariant Banach spaces, to the quasi-Banach case. Analogous properties are deduced for certain matrix classes. We use these results to prove that…

We give a complete characterization of the continuity of pseudodifferential operators with symbols in modulation spaces $M^{p,q}$, acting on a given Lebesgue space $L^r$. Namely, we find the full range of triples $(p,q,r)$, for which such a…

In the paper we extend the spectral invariance of pseudodifferential operators acting on (non-weighted) classical modulation spaces to allow the Lebesgue exponents to be smaller than one. These spaces occur naturally in approximation theory…

We deduce factorization properties for a quasi-Banach module over a quasi-Banach algebra. Especially we extend a result by Hewitt and prove that if any such algebra which possess a bounded left approximate identity, then any element in the…

In this paper we use Riesz spectral Theory and Gershgorin Theory to obtain explicit information concerning the spectrum of pseudo-differential operators defined on the unit circle $\mathbb{T} := \mathbb{R}/ 2 \pi \mathbb{ Z}$. For symbols…

We extend and improve the known results about the boundedness of the bilinear pseudo-differential operators with symbols in the bilinear H\"ormander class $BS^{m}_{0,0}(\mathbb{R}^n)$. We consider wider classes of symbols and improve…

We characterise the Schatten class $S^p$ properties of commutators $[b,T]$ of singular integrals and pointwise multipliers in a general framework of (quasi-)metric measure spaces. This covers, unifies, and extends a range of previous…

We deduce trace properties for modulation spaces of Gelfand-Shilov distributions. We use these properties to show that pseudo-differential operators with amplitudes in suitable modulation spaces, agree with pseudo-differential operators of…