Related papers: Projections, multipliers and decomposable maps on …

Normal elements (or multipliers) of the C* algebra of a certain class of locally compact groupoids admit a natural faithful representation as normal operators on the $L^2$-space of a dense orbit of the groupoid. We prove norm estimates on…

Let $S_n f$ be the $n$th partial sum of the Fourier series of a function $f$ in $L^1(\D)$, where $\D$ is the ring of integers of a local field $K$. For $1<p<\infty$, we characterize all weight functions $w$ so that the partial sum operators…

Let $G$ be a locally compact unimodular group, let $1\leq p<\infty$,let $\phi\in L^\infty(G)$ and assume that the Fourier multiplier $M_\phi$associated with $\phi$ is bounded on the noncommutative $L^p$-space $L^p(VN(G))$.Then $M_\phi\colon…

We develop a new transference method for completely bounded $L_p$-Fourier multipliers via proper cocycles arising from probability measure-preserving group actions. This method extends earlier results by Haagerup and Jolissaint, which were…

Our main result provides a closed expression for the completely bounded Fourier multiplier norm of the spherical functions on the generalized Lorentz groups. As a corollary, we find that there is no uniform bound on the completely bounded…

In this paper we study some estimates of norms in variable exponent Lebesgue spaces for maximal multiplier operators.We will consider the case when multiplier is the Fourier transform of a compactly supported Borel measure

We estimate the norms of many matrix coefficients of irreducible uniformly bounded representations of SL(2, R) as completely bounded multipliers of the Fourier algebra. Our results suggest that the known inequality relating the uniformly…

In this paper we discuss the $L^p$-$L^q$ boundedness of both spectral and Fourier multipliers on general locally compact separable unimodular groups $G$ for the range $1<p\leq q<\infty$. We prove a Lizorkin type multiplier theorem for…

Given two real numbers, the $L^2$ functions whose Fourier transforms vanish with a certain rapidity near the given numbers are characterised as those that are expressible as the sum of a certain number of generalised finite differences that…

We investigate the global continuity on $L^p$ spaces with $p\in [1,\infty]$ of Fourier integral operators with smooth and rough amplitudes and/or phase functions subject to certain non-degeneracy conditions. We initiate the investigation of…

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 show that the analyticity of semigroups $(T_t)_{t \geq 0}$ of selfadjoint contractive Fourier multipliers on $L^p$-spaces of compact abelian groups is preserved by the tensorisation of the identity operator of a Banach space for a large…

A result of Gilbert shows that every completely bounded multiplier $f$ of the Fourier algebra $A(G)$ arises from a pair of bounded continuous maps $\alpha,\beta:G \rightarrow K$, where $K$ is a Hilbert space, and $f(s^{-1}t) =…

We introduce partially defined Schur multipliers and obtain necessary and sufficient conditions for the existence of extensions to fully defined positive Schur multipliers, in terms of operator systems canonically associated with their…

Let G be a second countable, locally compact group and let f be a continuous Herz-Schur multiplier on G. Our main result gives the existence of a (not necessarily uniformly bounded) strongly continuous representation on a Hilbert space,…

We establish very general criteria for the existence of multiplication operators between noncommutative Orlicz spaces $L^{\psi_0}(\tM)$ and $L^{\psi_1}(\tM)$. We then show that these criteria contain existing results, before going on to…

It is known that the multiplier algebra of an approximately unital and nondegenerate $L^p$-operator algebra is again an $L^p$-operator algebra. In this paper we investigate examples that drop both hypotheses. In particular, we show that the…

We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue-Orlicz spaces of a discrete group and relative Toeplitz-Schur multipliers on Schatten-von-Neumann-Orlicz classes. Four applications are given:…

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…

In this paper, we establish an operator-valued Fourier multiplier theorem in weighted Lebesgue spaces, Besov and Triebel--Lizorkin spaces, assuming the multiplier has $\mathcal{R}$-bounded range and satisfies an $\ell^r$-summability…