Related papers: The multilinear Hormander multiplier theorem with …

We provide necessary and sufficient conditions for multilinear multiplier operators with symbols in $L^r$-based product-type Sobolev spaces uniformly over all annuli to be bounded from products of Hardy spaces to a Lebesgue space. We…

In a previous work we proved a spectral multiplier theorem of Mihlin--H\"ormander type for two-dimensional Grushin operators $-\partial_x^2 - V(x) \partial_y^2$, where $V$ is a doubling single-well potential, yielding the surprising result…

A function $q(x)$ is said to be a multiplier from the Sobolev space $H^\al_p(R^n)$ into $H^{-\al}_p(R^n)$ if the operator $Lf(x)=q(x)f(x)$ is a bounded operator from the first space into the second one. Let $M^\al_p$ the the space of such…

Let $G$ be the semidirect product $N \rtimes \mathbb{R}$, where $N$ is a stratified Lie group and $\mathbb{R}$ acts on $N$ via automorphic dilations. Homogeneous left-invariant sub-Laplacians on $N$ and $\mathbb{R}$ can be lifted to $G$,…

This 1995 paper contains a sharp version of the classical Marcinkiewicz multiplier theorem for the class of homogeneous Fourier multipliers in two dimensions; here a one-dimensional Marcinkiewicz condition is sufficient. Examples are given…

Bilinear Fourier multipliers of the form $e^{i (|\xi| + |\eta|+ |\xi + \eta|)} \sigma (\xi, \eta)$ are considered. It is proved that if $\sigma (\xi, \eta)$ is in the H\"ormander class $S^{m}_{1,0} (\mathbb{R}^{2n})$ with $m=-(n+1)/2$ then…

We prove a multiplier theorem of Mihlin-H\"ormander type for operators of the form $-\Delta_x - V(x) \Delta_y$ on $\mathbb{R}^{d_1}_x \times \mathbb{R}^{d_2}_y$, where $V(x) = \sum_{j=1}^{d_1} V_j(x_j)$, the $V_j$ are perturbations of the…

Given a bounded measurable function $\sigma$ on $\mathbb{R}^n$, we let $T_\sigma $ be the operator obtained by multiplication on the Fourier transform by $\sigma $. Let $0<s_1\le s_2\le \cdots \le s_n<1$ and $\psi$ be a Schwartz function on…

Let $f \in C^n(\mathbb{R})$ be such that $\Vert f^{(n)} \Vert_\infty < \infty$. Let $f^{[n]} \in C(\mathbb{R}^{n+1})$ be the $n$th order divided difference. A special case of our main result states that for $1 < p < \infty$ we have \[\Vert…

In the paper we study the multipliers of Fourier series in polynomials orthogonal in continuous-discrete Sobolev's spaces. Multiplier Theorem for Fourier-Sobolev series is obtained. This result is based on the representation of the Fej\'er…

We prove a sharp H\"ormander multiplier theorem for Schr\"odinger operators $H=-\Delta+V$ on $\mathbb{R}^n$. The result is obtained under certain condition on a weighted $L^\infty$ estimate, coupled with a weighted $L^2$ estimate for $H$,…

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…

Let $X$ be a space of homogeneous type and let $L$ be a nonnegative self-adjoint operator on $L^2(X)$ which satisfies a Gaussian estimate on its heat kernel. In this paper we prove a H\"omander type spectral multiplier theorem for $L$ on…

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 establish precise regularity conditions for $L_p$-boundedness of Fourier multipliers in the group algebra of $SL_n(\mathbf{R})$. Our main result is inspired by H\"ormander-Mikhlin criterion from classical harmonic analysis, although it…

We give a new proof of the boundedness of bilinear Schur multipliers of second order divided difference functions, as obtained earlier by Potapov, Skripka and Sukochev in their proof of Koplienko's conjecture on the existence of higher…

We prove spectral multiplier theorems for H\"ormander classes $\mathcal{H}^\alpha\_p$ for 0-sectorial operators A on Banach spaces assuming a bounded $H^\infty(\Sigma\_\sigma)$ calculus for some $\sigma \in (0,\pi)$ and norm and certain…

We develop a general framework for the analysis of operator-valued multilinear multipliers acting on Banach-valued functions. Our main result is a Coifman-Meyer type theorem for operator-valued multilinear multipliers acting on suitable…

In this paper we study sharp generalizations of $\dot{F}_p^{0,q}$ multiplier theorem of Mikhlin-H\"ormander type. The class of multipliers that we consider involves Herz spaces $K_u^{s,t}$. Plancherel's theorem proves…

This paper studies the $L^{p}$ boundedness of bilinear Fourier multipliers in the local $L^{2}$ range. We assume a H\"{o}rmander condition relative to a singular set that is a finite union of Lipschitz curves. The H\"{o}rmander condition is…