Related papers: Fourier multiplier theorems for Triebel-Lizorkin s…

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,…

We investigate the global boundedness of Fourier integral operators with amplitudes in the general H\"ormander classes $S^{m}_{\rho, \delta}(\mathbb{R}^n)$, $\rho, \delta\in [0,1]$ and non-degenerate phase functions of arbitrary rank…

We deduce continuity and (global) wave-front properties of classes of Fourier multipliers, pseudo-differential, and Fourier integral operators when acting on Orlicz spaces, or more generally, on Orlicz-Sobolev type spaces. In particular, we…

We consider certain Littlewood-Paley operators and prove characterization of some function spaces in terms of those operators. When treating weighted Lebesgue spaces, a generalization to weighted spaces will be made for H\"ormander's…

The paper focuses on the behaviour of unimodular Fourier multipliers with exponential growth in the context of weighted $L^p$-spaces. Our main result shows that much of the general theory of multipliers is approachable through the theory of…

We study the boundedness on the Wiener amalgam spaces $W^{p,q}_s$ of Fourier multipliers with symbols of the type $e^{i\mu(\xi)}$, for some real-valued functions $\mu(\xi)$ whose prototype is $|\xi|^{\beta}$ with $\beta\in (0,2]$. Under…

We prove a sharp multiplier theorem of Mihlin-H\"ormander type for the Grushin operator on the unit sphere in $\mathbb{R}^3$, and a corresponding boundedness result for the associated Bochner-Riesz means. The proof hinges on precise…

We present a multiplier theorem on anisotropic Hardy spaces. When $m$ satisfies the anisotropic, pointwise Mihlin condition, we obtain boundedness of the multiplier operator $T_m : H_A^p (\mathbb{R}^n) \rightarrow H_A^p (\mathbb{R}^n)$, for…

We show that maximal operators formed by dilations of Mikhlin-H"ormander multipliers are typically not bounded on $L^p(R^d)$. We also give rather weak conditions in terms of the decay of such multipliers under which $L^p$ boundedness of the…

On a general Lie group $G$ endowed with a sub-Riemannian structure and of local dimension $d$, we characterize the pointwise multipliers of Triebel--Lizorkin spaces $F^{p,q}_{\alpha}$ for $p,q\in (1,\infty)$ and $\alpha>d/p$, and those of…

We discuss the H\"ormander multiplier theorem for $L^p$ boundedness of Fourier multipliers in which the multiplier belongs to a fractional Sobolev space with smoothness $s$. We show that this theorem does not hold in the limiting case…

In this paper we extend classical Titchmarsh theorems on the Fourier transform of H$\ddot{\text{o}}$lder-Lipschitz functions to the setting of harmonic $NA$ groups, which relate smoothness properties of functions to the growth and…

On $\mathbb{R}^N$ equipped with a normalized root system $\mathcal R$ and a multiplicity function $k\geq 0$, let $dw(\mathbf x)=\Pi_{\alpha\in \mathcal R}|\langle \mathbf x,\alpha\rangle|^{k(\alpha)}\, d\mathbf x$,…

We develop a special multilinear complex interpolation theorem that allows us to prove an optimal version of the bilinear H\"ormander multiplier theorem concerning symbols that lie in the Sobolev space $L^r_s(\mathbb R^{2n})$, $2\le…

In this paper we study multipliers on graded nilpotent Lie groups defined via group Fourier transform. More precisely, we show that H\"ormander type conditions on the Fourier multipliers imply $L^p$-boundedness. We express these conditions…

We obtain restriction results of K. de Leeuw's type for maximal operators defined through multilinear Fourier multipliers of either strong or weak type acting on weighted Lebesgue spaces. We give some application of our development. In…

Any bounded linear operator $ T $ on $ L^2(\mathbb{R}^n) $ gives rise to the operator $ S= B \circ T \circ B^\ast $ on the Fock space $ \mathcal{F}(\C^n) $ where $ B $ is the Bargmann transform. In this article we identify those $ S $ which…

We investigate Fourier multipliers associated with the Strichartz Fourier transform on the Heisenberg group. In particular, we establish H\"ormander-type $L^{p}-L^{q}$ boundedness results for the range $1<p\leq 2\leq q<\infty$. The analysis…

Let $\mathcal{L} = -\partial_x^2 - V(x) \partial_y^2$ be the Grushin operator on $\mathbb{R}^2$ with coefficient $V : \mathbb{R} \to [0,\infty)$. Under the sole assumptions that $V(-x) \simeq V(x) \simeq xV'(x)$ and $x^2 |V''(x)| \lesssim…

We present a class of weight functions $ w$ on the circle $ \mathbb{T}$, called L\'evy-Khinchin-Schoenberg (LKS) weights, for which we are able to completely characterize (in terms of a capacitary inequality) all Fourier multipliers for the…