Related papers: Separating Fourier and Schur multipliers

In this paper we study the $L^p$-$L^q$ boundedness of the Fourier multipliers in the setting where the underlying Fourier analysis is introduced with respect to the eigenfunctions of an anharmonic oscillator $A$. Using the notion of a…

In this paper we study multiplication operators on Bergman spaces of high dimensional bounded domains and those von Neumann algebras induced by them via the geometry of domains and function theory of their symbols. In particular, using…

The author in $($On the order of Schur multiplier of non-abelian $p$-groups. J. Algebra (2009).322: 4479--4482$)$ showed that for any $p$-group $G$ of order $p^n$ there exists a nonnegative integer $s(G)$ such that the order of Schur…

We obtain bounds for the size of the Schur multiplier of finite $p$-groups and finite groups, which improve all existing bounds. Moreover, we obtain bounds for the size of the second cohomology group $H^2(G,\mathbb{Z}/p\mathbb{Z})$ of a…

In this paper we consider Fourier multiplier operators between vector-valued Besov spaces with different integrability exponents $p$ and $q$, which depend on the type $p$ and cotype $q$ of the underlying Banach spaces. In a previous paper…

Gonz\'alez-P\'erez, Parcet and Xia introduced recently a framework to study $L_p$-boundedness of certain families of idempotent multipliers on von Neumann algebras. It includes symbols $m\colon \mathrm{PSL}_2(\mathbb{C})\to \mathbb{R}$…

Let $X$ be a complete, simply connected harmonic manifold with sectional curvatures $K$ satisfying $K \leq -1$. In \cite{biswas6}, a Fourier transform was defined for functions on $X$, and a Fourier inversion formula and Plancherel theorem…

We consider a class of spectral multipliers on stratified Lie groups which generalise the class of H\"ormander multipliers and include multipliers with an oscillatory factor. Oscillating multipliers have been examined extensively in the…

Let $\Gamma < G$ be a discrete subgroup of a locally compact unimodular group $G$. Let $m\in C_b(G)$ be a $p$-multiplier on $G$ with $1 \leq p < \infty$ and let $T_{m}: L_p(\widehat{G}) \rightarrow L_p(\widehat{G})$ be the corresponding…

This is a survey on a notion of invariant operators, or Fourier multipliers on Hilbert spaces. This concept is defined with respect to a fixed partition of the space into a direct sum of finite dimensional subspaces. In particular this…

We prove $L^{p}$-boundedness of oscillating multipliers on some classes of rank one locally symmetric spaces.

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…

Let (X,m) and (Y,n) be standard measure spaces. A function f in $L^\infty(X\times Y,m\times n)$ is called a (measurable) Schur multiplier if the map $S_f$, defined on the space of Hilbert-Schmidt operators from $L_2(X,m)$ to $L_2(Y,n)$ by…

The Marcinkiewicz multipliers are $L^{p}$ bounded for $1<p<\infty $ on the Heisenberg group $\mathbb{H}^{n}\simeq \mathbb{C}^{n}\times \mathbb{R}$ (M\"uller, Ricci and Stein \cite{MRS}). This is surprising in the sense that these…

Let $G$ be a finite $p$-group of order $p^n$ and $M(G)$ be its Schur multiplier. It is well known result by Green that $|M(G)|= p^{\frac{1}{2}n(n-1)-t(G)}$ for some $t(G) \geq 0$. In this article we classify non-abelian $p$-groups $G$ of…

We investigate Fourier multipliers with smooth symbols defined over locally compact Hausdorff groups. Our main results in this paper establish new H\"ormander-Mikhlin criteria for spectral and non-spectral multipliers. The key novelties…

The paper concerns an analogue of the famous Schur multiplier in the context of associative algebras and a measure of how far its dimension is from being maximal. Applying a methodology from Lie theory, we characterize all…

An $S$-ring (a Schur ring) is said to be separable with respect to a class of groups $\mathcal{K}$ if every its algebraic isomorphism to an $S$-ring over a group from $\mathcal{K}$ is induced by a combinatorial isomorphism. We prove that…

In this article, we investigate the Schur multiplier of the special linear group $\mathrm{SL}_2(A)$ over finite commutative local rings $A$. We prove that the Schur multiplier of these groups is isomorphic to the $K$-group $K_2(A)$ whenever…

We show that a bilinear radial Fourier multiplier operator with symbol $\sigma$ is $L^2(\R^n)\times L^2(\R^n) \to L^1(\R^n)$ bounded, $n\in \mathbb N,$ if the function $\sigma$ satisfies the smoothness condition $\sigma(2^j\cdot)\Phi\in…