Related papers: (E,F)-multipliers and applications

For any positive integer $k$ and nonnegative integer $m$, we consider the symmetric function $G\left( k,m\right)$ defined as the sum of all monomials of degree $m$ that involve only exponents smaller than $k$. We call $G\left( k,m\right)$ a…

We investigate the problem of establishing bilateral continuous embeddings of the uniformly localized Bessel potential spaces $H^{\gamma}_{r, \: unif}(\mathbb{R}^n)$ into the multiplier spaces between Bessel potential spaces with positive…

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.

In this article we use the expansion for biquantization described in Cattaneo-Felder [math.QA/0309180] for the case of symmetric spaces. We introduce a function of two variables $E(X,Y)$ for any symmetric pairs. This function has an…

In this article, we present some results about Fourier multipliers on Hardy spaces in the product case. We mainly give descriptions of multipliers from the space $H^1(\mathbb{T}\times\mathbb{T})$ into the space $\ell^2$ and from the space…

For each pair $(m,n)$ of positive integers with $(m,n)\not= (1,1)$ and an arbitrary field $\bf F$ with algebraic closure $\overline{\bf F}$, let $\rm Po^{d,m}_n(\bf F)$ denote the space of $m$-tuples $(f_1(z),\cdots ,f_m(z))\in \bf F [z]^m$…

Let $\cal M$ be a semi-finite von Neumann algebra equipped with a distinguished faithful, normal, semi-finite trace $\tau$. We introduce the notion of equi-integrability in non-commutative spaces and show that if a rearrangement invariant…

Let $M_n$ denote the algebra of $n \times n$ complex matrices and let $\mathcal{A}\subseteq M_n$ be an arbitrary structural matrix algebra, i.e. a subalgebra of $M_n$ that contains all diagonal matrices. We consider injective maps $\phi :…

It is proved that for any free $\mathcal{A}$-modules $\mathcal{F}$ and $\mathcal{E}$ of finite rank on some $\mathbb{C}$-algebraized space $(X, \mathcal{A})$ a \textit{degenerate} bilinear $\mathcal{A}$-morphism $\Phi: \mathcal{F}\times…

We study the space of functions $\phi\colon \NN\to \CC$ such that there is a Hilbert space $H$, a power bounded operator $T$ in $B(H)$ and vectors $\xi,\eta$ in $H$ such that $$\phi(n) = < T^n\xi,\eta>.$$ This implies that the matrix…

For a locally compact group \(G\), let \(\mathcal{L}G\) denote its left group von Neumann algebra and let \(L^p(\mathcal{L}G)\), \(1 \le p \le \infty\), be the corresponding non-commutative \(L^p\)-space. Given \(\phi \in L^\infty(G)\), we…

We use the injective envelope to study quasimultipliers of operator spaces. We prove that all representable operator algebra products that an operator space can be endowed with are induced by quasimultipliers. We obtain generalizations 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…

The notion of invariant operators, or Fourier multipliers, is discussed for densely defined operators on Hilbert spaces, with respect to a fixed partition of the space into a direct sum of finite dimensional subspaces. As a consequence,…

The aim of this paper is to to show the admissibility of some class of Frechet spaces (see Definition 2.3). In particular, this generalizes the main results of [3]. As an application, we show the admissibility of a large class modular…

In the article, we find new dilatation results on non-commutative $L_p$ spaces. We prove that any selfadjoint, unital, positive measurable Schur multiplier on some $B(L^2(\Sigma))$ admits, for all $1\leq p<\infty$, an invertible isometric…

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…

For a free presentation $0 \to R \to F \to G \to 0$ of a Leibniz algebra $G$, the Baer invariant ${\cal M}^{\sf Lie}(G) = \frac{R \cap [F, F]_{Lie}}{[F, R]_{Lie}}$ is called the Schur multiplier of $G$ relative to the Liezation functor or…

The space of Bloch functions on bounded symmetric domains is extended by considering Bloch functions $f$ on the unit ball $B_E$ of finite and infinite dimensional complex Banach spaces in two different ways: by extending the classical Bloch…

Our primary objective in this article is to establish H\"ormander type $L^p \rightarrow L^q$ Fourier multiplier theorems in the context of noncompact type Riemannian symmetric spaces $\mathbb{X}$ of arbitrary rank for the range $1 < p \leq…