Related papers: Young's inequality for locally compact quantum gro…

We prove several results about the best constants in the Hausdorff-Young inequality for noncommutative groups. In particular, we establish a sharp local central version for compact Lie groups, and extend known results for the Heisenberg…

Those functions which nearly extremize Young's convolution inequality are characterized for discrete groups which have no nontrivial finite subgroups. Near-extremizers of the Hausdorff-Young inequality are characterized for Z^d.

The paper studies Hausdorff-Young inequalities for certain group extensions, by use of Mackey's theory. We consider the case in which the dual action of the quotient group is free almost everywhere. This result applies to yield a…

We generalize the Cauchy-Davenport theorem to locally compact groups.

We prove the classical Hausdorff-Young inequality for Orlicz spaces on compact homogeneous manifolds.

Using well-known techniques, we establish Hardy-Littlewood-type and Hausdorff-Young-type inequalities for generalized Gegenbauer expansions and their unification.

Young's convolution inequality provides an upper bound for the convolution of functions in terms of $L^p$ norms. It is known that for certain groups, including Heisenberg groups, the optimal constant in this inequality is equal to that for…

The generalized Young inequality on the Lorentz spaces for commutative hypergroups is introdused and an application of it is given to the theory of fractional integrals. The boundedness on the Lorentz space and the Hardy-Littlewood-Sobolev…

The classical Hausdorff-Young inequality for locally compact abelian groups states that, for $1\le p\le 2$, the $L^p$-norm of a function dominates the $L^q$-norm of its Fourier transform, where $1/p+1/q=1$. By using the theory of…

Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new inequalities improve Young's integral inequality on all time scales, such that the case where equality holds becomes particularly transparent…

The main purpose of this paper is to study the validity of the Hausdorff-Young inequality for vector-valued functions defined on a non-commutative compact group. The natural context for this research is that of operator spaces. This leads…

We investigate locally compact topological groups for which a generalized analogue of Heisenberg uncertainty inequality hold. In particular, it is shown that this inequality holds for $\mathbb{R}^n \times K$ (where $K$ is a separable…

In this short note we introduce a notion called "quantum injectivity" of locally compact quantum groups, and prove that it is equivalent to amenability of the dual. Particularly, this provides a new characterization of amenability of…

We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the…

We obtain Paley-type and Hausdorff-Young-Paley-type inequalities for Jacobi expansions.

In this paper we complete in several aspects the picture of locally compact quantum groups. First of all we give a definition of a locally compact quantum group in the von Neumann algebraic setting and show how to deduce from it a…

In recent years, various quantum inequalities have been established on quantum symmetries in the framework of quantum Fourier analysis. We provide a detailed introduction to quantum inequalities including Hausdorff-Young inequality, Young's…

We prove a generalized Fej\'er's theorem for locally compact groups.

We establish Paley-type and Hausdorff-Young-Paley-type inequalities for generalized Gegenbauer expansions.

Let $\mu$ be the Haar measure of a unimodular locally compact group $G$ and $m (G)$ as the infimum of the volumes of all open subgroups of $G$. The main result of this paper is that \begin{align*} \int_{G}^{} f \circ \left( \phi_1 * \phi_2…