Related papers: Spectral multipliers for wave operators

Consider the Schr\"odinger operator $\mathcal{L}=-\Delta+V$ in $\mathbb{R}^n, n\ge 3,$ where $V$ is a nonnegative potential satisfying a reverse H\"older condition of the type \begin{equation*} \left( \frac{1}{|B|}\int_B…

Let $0<\alpha<2$, $\beta>0$ and $\alpha/2<|s|\leq 1$. In a previous work, we obtained all possible values of the Lebesgue exponent $p=p(\gamma)$ for which the Fourier transform of $ E_{\alpha,\beta}(e^{\dot{\imath}\pi s} |\cdot|^{\gamma} )$…

On a compact Riemannian manifold with boundary, we prove a spectral inequality for the bi-Laplace operator in the case of so-called "clamped" boundary conditions , that is, homogeneous Dirichlet and Neumann conditions simultaneously. We…

We control a broad class of singular (or "rough") Fourier multipliers by geometrically-defined maximal operators via general weighted $L^2(\mathbb{R})$ norm inequalities. The multipliers involved are related to those of Coifman--Rubio de…

We prove that the noncommutative Lorentz norm (associated to a semifinite von Neumann algebra) of a propagator of the form $\varphi(|\mathscr{L}|)$ can be estimated if the modulus of the Borel function $\varphi$ is bounded by a continuous…

We study spectral subspaces of the Sturm-Liouville operator $f \mapsto -(pf')'$ on $\mathbb{R}$, where $p$ is a positive, piecewise constant function. Functions in these subspaces can be thought of as having a local bandwidth determined by…

Let X be a UMD space with type t and cotype q, and let T be a Fourier multiplier operator with a scalar-valued symbol m. If the Mihlin multiplier estimate holds for all partial derivatives of m up to the order n/max(t,q')+1, then T is…

We develop a technique of proving standard estimates in the setting of Laguerre function expansions of convolution type, which works for all admissible type multi-indices $\alpha$ in this context. This generalizes a simpler method existing…

Let $P(D)$ be the Laplacian $\Delta,$ or the wave operator $\square$. The following type of Carleman estimate is known to be true on a certain range of $p,q$: \[ \|e^{v\cdot x}u\|_{L^q(\mathbb{R}^d)} \le C\|e^{v\cdot…

Let $G$ be a locally compact unimodular group, and let $\phi$ be some function of $n$ variables on $G$. To such a $\phi$, one can associate a multilinear Fourier multiplier, which acts on some $n$-fold product of the non-commutative…

In this paper we develop the theory of Fourier multiplier operators $T_{m}:L^{p}(\mathbb{R}^{d};X)\to L^{q}(\mathbb{R}^{d};Y)$, for Banach spaces $X$ and $Y$, $1\leq p\leq q\leq \infty$ and $m:\mathbb{R}^d\to \mathcal{L}(X,Y)$ an…

Spectral operators of matrices proposed recently in [C. Ding, D.F. Sun, J. Sun, and K.C. Toh, Math. Program. {\bf 168}, 509--531 (2018)] are a class of matrix valued functions, which map matrices to matrices by applying a vector-to-vector…

In this paper, we introduce a family of Fourier multipliers using the spherical Fourier transform on Gelfand pairs. We refer to them as spherical Fourier multipliers. We study certain sufficient conditions under which they are bounded.…

In this paper we find new equivalent norms in $L^p(\mathbb{R}^n,\mathbb{B})$ by using multivariate Littlewood-Paley functions associated with Poisson semigroup for the Hermite operator, provided that $\mathbb{B}$ is a UMD Banach space with…

In this article mixed norm estimates are obtained for some integral operators, from which those for the Hermite semigroup and the Bochner Riesz means associated with the Hermite expansions are deduced. Also, mixed norm estimates for the…

We prove trace identities for commutators of operators, which are used to derive sum rules and sharp universal bounds for the eigenvalues of periodic Schroedinger operators and Schroedinger operators on immersed manifolds. In particular, we…

We introduce the concept of a spectral shift operator and use it to derive Krein's spectral shift function for pairs of self-adjoint operators. Our principal tools are operator-valued Herglotz functions and their logarithms. Applications to…

This paper concerns harmonic analysis of the Ornstein--Uhlenbeck operator L on the Euclidean space. We examine the method of decomposing a spectral multiplier \phi(L) into three parts according to the notion of admissibility, which…

We give characterizations of radial Fourier multipliers as acting on radial L^p-functions, 1<p<2d/(d+1), in terms of Lebesgue space norms for Fourier localized pieces of the convolution kernel. This is a special case of corresponding…

In this paper, Mikhlin and Marcinkiewicz--Lizorkin type operator-valued multiplier theorems in weighted Lebesgue-Bochner spaces are studied. By using this results embedding theorems in Sobolev-Lions type spaces is obtained. Moreover,…