Related papers: $L^p$-bounds for pseudo-differential operators on …
In this manuscript we provide necessary and sufficient conditions for the $\textnormal{weak}(1,p)$ boundedness, $1< p<\infty,$ of discrete Fourier multipliers (Fourier multipliers on $\mathbb{Z}^n$). Our main goal is to apply the results…
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…
A fundamental result in pseudodifferential theory is the Calder\'on-Vaillancourt theorem, which states that a pseudodifferential operator defined from a H\"ormander symbol of order $0$ defines a bounded operator on $L^2(\mathbb{R}^d)$. In…
In this paper, we study the boundedness of pseudo-differential operators with symbols in $S_{\rho,\delta}^m$ on the modulation spaces $M^{p,q}$. We discuss the order $m$ for the boundedness $\mathrm{Op}(S_{\rho,\delta}^m) \subset…
Consider a non-negative self-adjoint operator $H$ in $L^2(\mathbb{R}^d)$. We suppose that its heat operator $e^{-tH}$ satisfies an off-diagonal algebraic decay estimate, for some exponents $p_0\in[0,2)$. Then we prove sharp $L^p\to L^p$…
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…
We study the boundedness of rough Fourier integral and pseudodifferential operators, defined by general rough H\"ormander class amplitudes, on Banach and quasi-Banach $L^p$ spaces. Thereafter we apply the aforementioned boundedness in order…
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…
This work is concerned with extending the results of Calder\' on and Vaillancourt proving the boundedness of Weyl pseudo differential operators Op_h^{weyl} (F) in L^2(\R^n). We state conditions under which the norm of such operators has an…
The sharp range of $L^p$-estimates for the class of H\"ormander-type oscillatory integral operators is established in all dimensions under a general signature assumption on the phase. This simultaneously generalises earlier work of the…
In this article, we investigate the unweighted and weighted $L^p$-boundedness of pseudo-multipliers associated with a class of Schr\"odinger operators. The weight classes we consider are tailored to this framework and strictly contain the…
In this paper, we consider the $L^2$-boundedness of pseudo-differential operators with symbols in $\alpha$-modulation spaces.
On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct a pseudodifferential extension that reflects this behaviour. In the…
We prove some $L^p$-Liouville theorems for hypoelliptic second order Partial Differential Operators left translation invariant with respect to a Lie group composition law in $\mathbb{R}^n$. Results for both solutions and subsolutions are…
Given a complex, elliptic coefficient function we investigate for which values of $p$ the corresponding second-order divergence form operator, complemented with Dirichlet, Neumann or mixed boundary conditions, generates a strongly…
In this paper we develop the functional calculus for elliptic operators on compact Lie groups without the assumption that the operator is a classical pseudo-differential operator. Consequently, we provide a symbolic descriptions of complex…
We consider here pseudo-differential operators whose symbol $\sigma(x,\xi)$ is not infinitely smooth with respect to $x$. Decomposing such symbols into four -sometimes five- components and using tools of paradifferential calculus, we derive…
On the torus, it is possible to assign a global symbol to a pseudodifferential operator using Fourier series. In this paper we investigate the relations between the local and global symbols for the operators in the classical H\"ormander…
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 prove an $L^p$-spectral multiplier theorem for sub-Laplacians on Heisenberg type groups under the sharp regularity condition $s>d\left|1/p-1/2\right|$, where $d$ is the topological dimension of the underlying group. Our approach relies…