Related papers: $L^p$-bounds for pseudo-differential operators on …

We generalize the idea of a multiplier in two different ways and generalize a recent result of Geiss, Montomery-Smith and Saksman. First of all, we consider multipliers in the form of a vector acting on a scalar function. Using this…

In this paper, we give a sharp sparse domination of pseudodifferential operators associated with symbols belonging to the H\"{o}rmander class, and fundamental solutions of dispersive equations. Furthermore, we give boundedness results of…

Pseudo-differential and Fourier series operators on the n-torus are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal symbols are investigated and the correspondence…

In this article, we begin a systematic study of the boundedness and the nuclearity properties of multilinear periodic pseudo-differential operators and multilinear discrete pseudo-differential operators on $L^p$-spaces. First, we prove…

In this article, we obtain new results for Fourier restriction type problems on compact Lie groups. We first provide a sharp form of $L^p$ estimates of irreducible characters in terms of their Laplace-Beltrami eigenvalue and as a…

We consider a class of degenerate Ornstein-Uhlenbeck operators in $\mathbb{R}^{N}$, of the kind \[ \mathcal{A}\equiv\sum_{i,j=1}^{p_{0}}a_{ij}\partial_{x_{i}x_{j}}^{2} +\sum_{i,j=1}^{N}b_{ij}x_{i}\partial_{x_{j}}% \] where $(a_{ij})…

Boundedness properties for pseudodifferential operators with symbols in the bilinear H\"ormander classes of sufficiently negative order are proved. The results are obtained in the scale of Lebesgue spaces and, in some cases, end-point…

In this article we deal with a variation of a theorem of Mauceri concerning the $ L^p $ boundedness of operators $ M $ which are known to be bounded on $ L^2.$ We obtain sufficient conditions on the kernel of the operaor $ M $ so that it…

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.…

Let $X$ be a compact manifold with boundary. Suppose that the boundary is fibred, $\phi:\pa X\longrightarrow Y,$ and let $x\in\CI(X)$ be a boundary defining function. This data fixes the space of `fibred cusp' vector fields, consisting of…

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…

In this work we establish a subelliptic sharp G\r{a}rding inequality on compact Lie groups for pseudo-differential operators with symbols belonging to global subelliptic H\"ormander classes. In order for the inequality to hold we require…

For a limited range of indices $p$, we obtain $L^p(\mathbb{R}^n)$ boundedness for singular integral operators whose kernels satisfy a condition weaker than the typical H\"ormander smoothness estimate. These operators are assumed to be…

We develop an $L^p(\mathbb{R}^n)$-functional calculus appropriated for interpreting "non-classical symbols" of the form $a(-\Delta)$, and for proving existence in $L^q(\mathbb{R}^n)$, some $q > p$, of solutions to nonlinear…

In this note we study the analytical index of pseudo-differential operators by using the notion of (infinite dimensional) operator-valued symbols (in the sense of Ruzhansky and Turunen). Our main tools will be the McKean-Singer index…

We extend the estimates proved by Donnelly and Fefferman and by Lebeau and Robbiano for sums of eigenfunctions of the Laplacian (on a compact manifold) to estimates for sums of eigenfunctions of any positive and elliptic pseudo-differential…

We consider singular integral operators and maximal singular integral operators with rough kernels on homogeneous groups. We prove certain estimates for the operators that imply $L^p$ boundedness of them by an extrapolation argument under a…

We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$, then a pseudodifferential operator $\operatorname{Op}(a)$ is bounded on…

We consider the bilinear pseudo-differential operators with symbols in the bilinear H\"ormander classes $BS_{\rho, \rho}^m$, $0 < \rho < 1$. In this paper, we show that the condition $1/p = 1/p_1 + 1/p_2$ is necessary when we consider the…