Related papers: Closable Multipliers

This paper discusses the boundedness of the trilinear multiplier operator $T_{m}(f_1,f_2,f_3)$, when the multiplier satisfies a certain degree of smoothness but with no decaying condition and is $L^{q}$-integrable with an admissible range…

The properties of the maximal operator of the $(C,\alpha)$-means ($\alpha=(\alpha_1,\ldots,\alpha_d)$) of the multi-dimensional Walsh-Kaczmarz-Fourier series are discussed, where the set of indices is inside a cone-like set. We prove that…

We describe the multiplier algebra of the noncommutative Schwartz space. This multiplier algebra can be seen as the largest ${}^*$-algebra of unbounded operators on a separable Hilbert space with the classical Schwartz space of rapidly…

A mapping $f:X\to Y$ between metric spaces is called \emph{little Lipschitz} if the quantity $$ \operatorname{lip}(f(x)=\liminf_{r\to0}\frac{\operatorname{diam} f(B(x,r))}{r} $$ is finite for every $x\in X$. We prove that if a compact (or,…

We establish an unbounded version of Stinespring's Theorem and a lifting result for Stinespring representations of completely positive modular maps defined on the space of all compact operators. We apply these results to study positivity…

The objective of this paper is to study wandering subspaces for commuting tuples of bounded operators on Hilbert spaces. It is shown that, for a large class of analytic functional Hilbert spaces $\mathcal{H}_K$ on the unit ball in $\mathbb…

We give a contractive Schur multiplier characterization of locally compact groups coarsely embeddable into Hilbert spaces. Consequently, all locally compact groups whose weak Haagerup constant is 1 embed coarsely into Hilbert spaces, and…

We study in this paper analytic Schur multipliers on ${\Bbb C}_+^2$ and ${\Bbb D}^2$, i.e. Schur multipliers on ${\Bbb R}^2$ and ${\Bbb T}^2$ that are boundary-value functions of functions analytic in ${\Bbb C}_+^2$ and ${\Bbb D}^2$. Such…

In this paper, we will study the strong type and weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_\lambda$-function on the generalized Morrey spaces $L^{p,\Phi}$ for…

We show that if (M,\omega) is a closed symplectic manifold which admits a nontrivial Hamiltonian vector field all of whose contractible closed orbits are constant, then Hofer's metric on the group of Hamiltonian diffeomorphisms of…

We provide characterizations for boundedness of multilinear Fourier operators on Hardy-Lebesgue spaces with symbols locally in Sobolev spaces. Let $H^q(\mathbb R^n)$ denote the Hardy space when $0<q\le 1$ and the Lebesgue space $L^q(\mathbb…

We introduce multidimensional Schur multipliers and characterise them generalising well known results by Grothendieck and Peller. We define a multidimensional version of the two dimensional operator multipliers studied recently by Kissin…

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 prove that the existence of a Mihlin-H\"ormander functional calculus for an operator $L$ implies the boundedness on $L^p$ of both the maximal operators and the continuous square functions build on spectral multipliers of $L.$ The…

This paper offers a unified approach to determining when two generalized Toeplitz operators on L^2 are equivalent. This will be done through multipliers between closed subspaces of L^2. Our discussion will include Toeplitz operators (and…

It follows, from a generalised version of Paley-Wiener theorem, that the Laplace transform is an isometry between certain spaces of weighted $L^2$ functions defined on $(0, \infty)$ and (Hilbert) spaces of analytic functions on the right…

For $\alpha>-1$, let $A^2_{\alpha}$ be the corresponding weighted Bergman space of the unit ball in $\mathbb{C}^n$. For a bounded measurable function $f$, let $T_f$ be the Toeplitz operator with symbol $f$ on $A^2_{\alpha}$. This paper…

We show that capacity can be computed with locally Lipschitz functions in locally complete and separable metric spaces. Further, we show that if $(X,d,\mu)$ is a locally complete and separable metric measure space, then continuous functions…

A function $q(x)$ is said to be a multiplier from the Sobolev space $H^\al_p(R^n)$ into $H^{-\al}_p(R^n)$ if the operator $Lf(x)=q(x)f(x)$ is a bounded operator from the first space into the second one. Let $M^\al_p$ the the space of such…

A function F:R^2->R is sup-measurable if F_f:R->R given by F_f(x)=F(x,f(x)), x in R, is measurable for each measurable function f:R->R. It is known that under different set theoretical assumptions, including CH, there are sup-measurable…