Related papers: Spectral multipliers for wave operators

Let $\mathscr{L}$ be a smooth second-order real differential operator in divergence form on a manifold of dimension $n$. Under a bracket-generating condition, we show that the ranges of validity of spectral multiplier estimates of…

We prove an $L^p$-spectral multiplier theorem under the sharp regularity condition $s > d\left|1/p - 1/2\right|$ for sub-Laplacians on M\'etivier groups. The proof is based on a restriction type estimate which, at first sight, seems to be…

We describe a simple but surprisingly effective technique of obtaining spectral multiplier results for abstract operators which satisfy the finite propagation speed property for the corresponding wave equation propagator. We show that, in…

We investigate a class of spectral multipliers for an Ornstein-Uhlenbeck operator $\mathcal L$ in $\mathbb R^n$, with drift given by a real matrix $B$ whose eigenvalues have negative real parts. We prove that if $m$ is a function of Laplace…

Let $L$ be a non-negative self adjoint operator acting on $L^2(X)$ where $X$ is a space of homogeneous type. Assume that $L$ generates a holomorphic semigroup $e^{-tL}$ whose kernels $p_t(x,y)$ satisfy generalized $m$-th order Gaussian…

We obtain a general Marcinkiewicz-type multiplier theorem for mixed systems of strongly commuting operators $L=(L_1,...,L_d);$ where some of the operators in $L$ have only a holomorphic functional calculus, while others have additionally a…

We prove an $L^p$ spectral multiplier theorem for functions of the $K$-invariant sublaplacian $L$ acting on the space of functions of fixed $K$-type on the group $SL(2,\mathbb{R}).$ As an application we compute the joint…

We study a class of spectral multipliers \phi(L) for the Ornstein--Uhlenbeck operator L arising from the Gaussian measure on R^n and find a sufficient condition for integrability of \phi(L)f in terms of the admissible conical square…

Let $G = N \rtimes A$, where $N$ is a stratified group and $A = \mathbb{R}$ acts on $N$ via automorphic dilations. Homogeneous sub-Laplacians on $N$ and $A$ can be lifted to left-invariant operators on $G$ and their sum is a sub-Laplacian…

Our primary objective in this article is to establish H\"ormander type $L^p \rightarrow L^q$ Fourier multiplier theorems in the context of noncompact type Riemannian symmetric spaces $\mathbb{X}$ of arbitrary rank for the range $1 < p \leq…

From a theorem of Christ and Mauceri and Meda it follows that, for a homogeneous sublaplacian $L$ on a $2$-step stratified group $G$ with Lie algebra $\mathfrak{g}$, an operator of the form $F(L)$ is of weak type $(1,1)$ and bounded on…

In this paper we discuss the $L^p$-$L^q$ boundedness of both spectral and Fourier multipliers on general locally compact separable unimodular groups $G$ for the range $1<p\leq q<\infty$. We prove a Lizorkin type multiplier theorem for…

We investigate H\"ormander spectral multiplier theorems as they hold on $X = L^p(\Omega),\: 1 < p < \infty,$ for many self-adjoint elliptic differential operators $A$ including the standard Laplacian on $\R^d.$ A strengthened matricial…

We consider degenerate differential operators $A = \displaystyle{\sum_{k,j=1}^d \partial_k (a_{kj} \partial_j)}$ on $L^2(\mathbb{R}^d)$ with real symmetric bounded measurable coefficients. Given a function $\chi \in…

Let $L$ be a homogeneous sublaplacian on a 2-step stratified Lie group $G$ of topological dimension $d$ and homogeneous dimension $Q$. By a theorem due to Christ and to Mauceri and Meda, an operator of the form $F(L)$ is bounded on $L^p$…

For any bounded, regulated function $m: [0,\infty) \to \mathbb{C}$, consider the family of operators $\{ T_R \}$ on the sphere $S^d$ such that $T_R f = m(k/R) f$ for any spherical harmonic $f$ of degree $k$. We completely characterize the…

Let $A$ be a $0$-sectorial operator with a bounded $H^\infty(\Sigma\_\sigma)$-calculus for some $\sigma \in (0,\pi),$ e.g. a Laplace type operator on $L^p(\Omega),\: 1 < p < \infty,$ where $\Omega$ is a manifold or a graph. We show that $A$…

We extend several fundamental estimates regarding spectral multipliers for the free Laplacian on $\mathbb R^3$ to the case of perturbed Hamiltonians of the form $-\Delta+V$, where $V$ is a scalar real-valued potential. In this paper, we…

Let $X$ be a space of homogeneous type and let $L$ be an injective, non-negative, self-adjoint operator on $L^2(X)$ such that the semigroup generated by $-L$ fulfills Davies-Gaffney estimates of arbitrary order. We prove that the operator…

In this paper, we introduce a criterion for maximal operators associated with Fourier multipliers to be bounded on $L^p(\mathbb{R}^d)$. Noteworthy examples satisfying the criterion are multipliers of the Mikhlin type or limited decay which…