Related papers: On Schatten-von Neumann class properties of pseudo…
Let $G$ be a unimodular type I second countable locally compact group and $\hat G$ its unitary dual. We introduce and study a global pseudo-differential calculus for operator-valued symbols defined on $G\times\hat G$, and its relations to…
We define and study pseudo-differential operators on a class of fractals that include the post-critically finite self-similar sets and Sierpinski carpets. Using the sub-Gaussian estimates of the heat operator we prove that our operators…
We introduce a simplified (coarse) version of pseudo-differential calculus for operators of order zero on complete Riemannian manifolds. This calculus works for the usual Hormander (1,0) class of operators, as well as for…
We consider bilinear pseudo-differential operators with symbols in the bilinear H\"ormander class, $BS_{\rho, \rho}^m$, $m \in \mathbb{R}$, $0 \leq \rho < 1$. The aim of this paper is to discuss low regularity conditions for symbols to…
This is a continuation of our paper \cite{AP2}. We prove that for functions $f$ in the H\"older class $\L_\a(\R)$ and $1<p<\be$, the operator $f(A)-f(B)$ belongs to $\bS_{p/\a}$, whenever $A$ and $B$ are self-adjoint operators with…
Time-frequency analysis have played a crucial role in the development of localization operators in the last twenty years. We present its applications to the study of boundedness and Schatten Class property for such operators. In particular,…
We characterize the membership of Hankel operators with general symbols in the Schatten Classes $S^p,\, p\in(0,1),$ of the large Bergman spaces $A^2_{\omega}$. The case $p\geq 1$ was proved by Lin and Rochberg.
In this paper we expand on B.-W. Schulze's abstract edge pseudodifferential calculus and introduce a larger class of operators that is modeled on H\"ormander's $\varrho,\delta$ calculus, where $0 \leq \delta < \varrho \leq 1$. This…
In this work we characterise the H\"ormander classes $\symbClassOn{m}{\rho}{\delta}{\group,\textnormal{H\"or}}$ on the open manifold $\group = (-1,1)^n$. We show that by endowing the open manifold $\group = (-1,1)^n$ with a group structure,…
We introduce and study a new class of pseudo-differential operators associated with a fractional Hankel--Bessel transform. Motivated by the classical Hankel transform and the pseudo-differential operators associated with Bessel operators…
Given a compact Lie group $G$ and its unitary dual $\widehat{G}$, we establish the weak (1,1) continuity for pseudo-differential operators in the global H\"ormander classes of order $-n(1-\rho)/2$ on $G\times \widehat{G}$. Our approach…
We study trace ideal properties of the commutators $[(-\Delta)^{\frac{\epsilon}{2}},M_f]$ of a power of the Laplacian with the multiplication operator by a function $f$ on $\mathbb R^d$. For a certain range of $\epsilon\in\mathbb R$, we…
We develop a new method for obtaining bounds on the negative eigenvalues of self-adjoint operators B in terms of a Schatten norm of the difference of the semigroups generated by A and B, where A is an operator with non-negative spectrum.…
In this note we present a symbolic pseudo-differential calculus on the Heisenberg group. We particularise to this group our general construction [4,3,2] of pseudo-differential calculi on graded groups. The relation between the Weyl…
We obtain weighted $L^p$ inequalities for pseudo-differential operators with smooth symbols and their commutators by using a class of new weight functions which include Muckenhoupt weight functions. Our results improve essentially some…
The study of Schatten classes has a long tradition in geometric functional analysis and related fields. In this paper we study a variety of geometric and probabilistic aspects of finite-dimensional Schatten classes of not necessarily square…
In this Note, we present a Calder\'on-type uniqueness theorem on the Cauchy problem of stochastic partial differential equations. To this aim, we introduce the concept of stochastic pseudo-differential operators, and establish their…
A generalization of differential operators are pseudodifferential operators which are used for reasoning about partial differential equations with variable coefficients. A lot of useful properties about classical pseudodifferential…
We introduce new classes of modulation spaces over phase space. By means of the Kohn-Nirenberg correspondence, these spaces induce norms on pseudo-differential operators that bound their operator norms on $L^p$-spaces, Sobolev spaces, and…
We extended the known result that symbols from modulation spaces $M^{\infty,1}(\mathbb{R}^{2n})$, also known as the Sj\"{o}strand's class, produce bounded operators in $L^2(\mathbb{R}^n)$, to general $L^p$ boundedness at the cost of lost of…