Related papers: Fourier multipliers on a vector-valued function sp…

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 consider Haar multiplier operators $T_m$ acting on Sobolev spaces, and more generally Triebel-Lizorkin spaces $F^s_{p,q}(\mathbb{R})$, for indices in which the Haar system is not unconditional. When $m$ depends only on the Haar…

We investigate the boundedness of Fourier multipliers on a compact Lie group when acting on Triebel-Lizorkin spaces. Criteria are given in terms of the H\"ormander-Mihlin-Marcinkiewicz condition. In our analysis, we use the difference…

We describe the idempotent Fourier multipliers that act contractively on $H^p$ spaces of the $d$-dimensional torus $\mathbb{T}^d$ for $d\geq 1$ and $1\leq p \leq \infty$. When $p$ is not an even integer, such multipliers are just…

The present paper, is devoted to investigation of operator--valued Fourier multiplier theorems from $B_{q_{1},r}^{s}$ to $B_{q_{2},r}^{s}$, optimal embedding of Besov spaces, the separability and positivity of differential operators. Here,…

We prove various extensions of the Coifman-Rubio de Francia-Semmes multiplier theorem to operator-valued multipliers on Banach function spaces. Our results involve a new boundedness condition on sets of operators which we call…

Consider the multidimensional Bessel operator $$B f(x) = -\sum_{j=1}^N \left(\partial_j^2 f(x) +\frac{\alpha_j}{x_j} \partial_j f(x)\right), \quad x\in(0,\infty)^N. $$ Let $d = \sum_{j=1}^N \max(1,\alpha_j+1)$ be the homogeneous dimension…

In this paper, we study properties of the bilinear multiplier space. We give a necessary condition for a continuous integrable function to be a bilinear multiplier on variable exponent Lebesgue spaces. And we prove the localization theorem…

We study a.e. convergence on $L^p$, and Lorentz spaces $L^{p,q}$, $p>\tfrac{2d}{d-1}$, for variants of Riesz means at the critical index $d(\tfrac 12-\tfrac 1p)-\tfrac12$. We derive more general results for (quasi-)radial Fourier…

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…

We prove multiplier theorems on rank one noncompact symmetric spaces which improve aspects of existing results. A common theme of our main results is that we partially drop specific assumptions on the multiplier function such as a…

Conditions for a function (number sequence) to be a multiplier on the space of integrable functions on $\Bbb R$ ($\Bbb T$) are given. This generalizes recent results of Giang and Moricz.

Inspired by the work of A. Bonami and S. Poornima that a non-constant function which is homogeneous of degree $0$ cannot be a Fourier multiplier on homogeneous Sobolev spaces, we establish analogous results for Fourier multipliers on the…

In this paper we proof that every Fourier multiplier on homogeneous sobolev space $\dot{W}_1^1(\mathbb{R}^d)$ is a continuous function. Our theorem is generalization of A. Bonami and S. Poornima result for Fourier multipliers, which are…

We find that if a Fourier multiplier is continuous from $L^{\Phi_1}$ to $L^{\Phi_2}$, then it is also continuous from $M^{\Phi_1,\Psi}$ to $M^{\Phi_2,\Psi}$, where $\Phi_1,\Phi_2,\Psi$ are quasi-Young functions and $\Phi_1$ fulfills the…

In this paper we present (quasi-)norm equivalence on a vector-valued function space $L^p_A(l^q)$ and extend the equivalence to $p=\infty$ and $0<q<\infty$ in the scale of Triebel-Lizorkin space, motivated by Fraizer-Jawerth. By applying the…

This work characterizes the multipliers on vector-valued Hardy spaces over the infinite polydisk and the infinite polytorus, as well as in the context of Dirichlet series. Unlike the scalar-valued setting, where these frameworks are…

We prove higher summability for the gradient of minimizers of strongly convex integral functionals of the Calculus of Variations with (p,q)-Growth conditions in low dimension. Our procedure is set in the framework of Fractional Sobolev…

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…

We consider different characterizations of Triebel--Lizorkin type spaces of analytic functions on the unit disc. Even though our results appear in the folklore, detailed descriptions are hard to find, and in fact we are unable to discuss…