Related papers: $L^p$-$L^q$ multipliers on locally compact groups

Let G be a locally compact group, and let 1 < p < \infty. In this paper we investigate the injectivity of the left L^1(G)-module L^p(G). We define a family of amenability type conditions called (p,q)-amenability, for any 1 <= p <= q. For a…

Let $L$ be a non-negative self-adjoint operator on $L^2(X)$. Assume that operator $L$ generates the analytic semigroup $\{e^{-tL}\}_{t>0}$ whose kernels satisfy the standard Gaussian upper bounds. This paper investigates the sharp weighted…

In this paper we study maximal directional singular integral operators in $ \mathbb{R}^n $ given by a H\"ormander--Mihlin multiplier on an $ (n-1)$-dimensional subspace and acting trivially in the perpendicular direction. The subspace is…

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 find optimal conditions on $m$-linear Fourier multipliers to give rise to bounded operators from a product of Hardy spaces $H^{p_j}$, $0<p_j\le 1$, to Lebesgue spaces $L^p$. The conditions we obtain are necessary and sufficient for…

From a theorem of Christ and Mauceri and Meda it follows that, for a homogeneous sublaplacian $L$ on a $2$-step stratified group $G$ with Lie algebra $\mathfrak{g}$, an operator of the form $F(L)$ is of weak type $(1,1)$ and bounded on…

For any bounded, regulated function $m: [0,\infty) \to \mathbb{C}$, consider the family of operators $\{ T_R \}$ on the sphere $S^d$ such that $T_R f = m(k/R) f$ for any spherical harmonic $f$ of degree $k$. We completely characterize the…

We complement the recent theory of general singular integrals $T$ invariant under the Zygmund dilations $(x_1, x_2, x_3) \mapsto (s x_1, tx_2, st x_3)$ by proving necessary and sufficient conditions for the boundedness and compactness of…

We study the class $\mathcal{M}_p$ of Schur multipliers on the Schatten-von Neumann class $\mathcal{S}_p$ with $1 \leq p \leq \infty$ as well as the class of completely bounded Schur multipliers $\mathcal{M}_p^{cb}$. We first show that for…

We prove a weighted inequality which controls conic Fourier multiplier operators in terms of lacunary directional maximal operators. By bounding the maximal operators, this enables us to conclude that the multiplier operators are bounded on…

We introduce C*-pseudo-multiplicative unitaries and concrete Hopf C*-bimodules for the study of quantum groupoids in the setting of C*-algebras. These unitaries and Hopf C*-bimodules generalize multiplicative unitaries and Hopf C*-algebras…

Let G be a locally compact Hausdorff group in which every element is of finite order, and let P(G) denote the class of all regular probability measures on G. In this note, it is observed that a characterization of algebraically regular…

In the setting of von Neumann algebras, measurable quantum groupoids have successfully been axiomatized and studied by Enock, Vallin, and Lesieur, whereas in the setting of $C^{*}$-algebras, a similar theory of locally compact quantum…

We study multiplier theorems on a vector-valued function space, which is a generalization of the results of Calder\'on-Torchinsky and Grafakos-He-Honz\'ik-Nguyen, and an improvement of the result of Triebel. For $0<p<\infty$ and $0<q\leq…

Let $G$ be a locally compact group and $1\leq p<\infty$. A continuous unitary representation $\pi\!: G\to B(\mathcal{H})$ of $G$ is an $L^p$-representation if the matrix coefficient functions $s\mapsto \langle \pi(s)x,x\rangle$ lie in…

In this paper we establish $L^p(\mathbb{R}^d,\gamma_\infty)$-boundedness properties for square functions involving time and spatial derivatives of Ornstein-Uhlenbeck semigroups. Here $\gamma_\infty$ denotes the invariant measure. In order…

We study Calder\'on-type commutators $[M_b,T_i\mathcal R_j]$ in the rational Dunkl setting with a finite reflection group $G$. If $b$ belongs to the orbit Lipschitz class $\operatorname{Lip}_d$, then for every $1<p<\infty$ we prove…

In this paper we establish $L^p$-boundedness properties for Laplace type transform spectral multipliers associated with the Schr\"odinger operator $\mathcal{L}=-\Delta +V$. We obtain for this type of multipliers pointwise representation as…

Let $G$ be a $2$-step stratified group of topological dimension $d$ and homogeneous dimension $Q$. Let $L$ be a homogeneous sub-Laplacian on $G$. By a theorem due to Christ and to Mauceri and Meda, an operator of the form $F(L)$ is of weak…

In this work, we introduce a class of Timmermann's measured multiplier Hopf *-algebroids called algebraic quantum transformation groupoids of compact type. Each object in this class admits a Pontrjagin-like dual called an algebraic quantum…