Related papers: The Hausdorff-Young inequality on Lie groups

We discuss a Moser type argument to show when a deformation of a Lie group homomorphism and of a Lie subgroup is trivial. For compact groups we obtain stability results.

We suggest a new algorithm to estimate representations of compact Lie groups from finite samples of their orbits. Different from other reported techniques, our method allows the retrieval of the precise representation type as a direct sum…

In this paper, we examine Lie group actions on moduli spaces (sets themselves built as quotients by group actions) and their fixed points. We show that when the Lie group is compact and connected, we obtain a linear constraint. This…

We determine the optimal orders for the best constants in the non-commutative Burkholder-Gundy, Doob and Stein inequalities obtained recently in the non-commutative martingale theory.

We initiate the study of quadratic discrepancy for finite point sets on the Heisenberg group $\mathbb H^n$ with respect to upper Ahlfors regular probability measures. For a natural family of test sets given by left translations and…

Following (Shevtsova, 2010) we introduce detailed classification of the asymptotically exact constants in natural estimates of the rate of convergence in the Lindeberg central limit theorem, namely in Esseen's, Rozovskii's, and Wang-Ahmad's…

Hrushovski proved the Lie model theorem in full generality with model theoretic methods. The theorem states that for every approximate group there exists a generalized definable locally compact model, which, simplifying, is a…

When a discrete group admits a convex-cocompact action on a non-compact rank-one symmetric space, there is a natural lower bound for the Hausdorff dimension of the limit set, given by the Ahlfors regular conformal dimension of the boundary…

This paper proves existence of optimizers of the Stein-Weiss inequalities on Carnot groups under some conditions. The adjustment of Lions' concentration compactness principles to Carnot groups plays an important role in our proof. Unlike…

The classical Hausdorff-Young inequalities for the Fourier transform acting between appropriate $L_p$ spaces are cornerstones of Fourier analysis. Here we extend it to weighted spaces of Besov or Sobolev type where the weight has the form…

We prove a Payne-Weinberger type inequality for the $p$-Laplacian Neumann eigenvalues ($p\ge 2$). The inequality provides the sharp upper bound on convex domains, in terms of the diameter alone, of the best constants in Poincar\'e…

We describe the structure of Hausdorff locally compact semitopological $0$-bisimple inverse $\omega$-semigroups with compact maximal subgroups. In particular, we show that a Hausdorff locally compact semitopological $0$-bisimple inverse…

We study autocorrelation inequalities, in the spirit of Barnard and Steinerberger's work. In particular, we obtain improvements on the sharp constants in some of the inequalities previously considered by these authors, and also prove…

In this paper we provide another way to deduce the Loomis-Whitney inequality on higher dimensional Heisenberg groups $\mathbb{H}^n$ based on the one on the first Heisenberg group $\mathbb{H}^1$ and the known nonlinear Loomis-Whitney…

Let G be a Lie group over a local field of positive characteristic which admits a contractive automorphism f (i.e., the forward iterates f^n(x) of each group element x converge to the neutral element 1). We show that then G is a torsion…

We prove an optimal lower bound for the best constant in a class of weighted anisotropic Poincar\'e inequalities

In this work, we establish a mixed local--nonlocal Sobolev-type inequality in the Heisenberg group and demonstrate that its extremals coincide with solutions to the corresponding mixed local--nonlocal singular $p$-Laplace equations. We…

We study the horofunction boundary of finitely generated nilpotent groups, and the natural group action on it. More specifically, we prove the followings results: For discrete Heisenberg groups, we classify the orbits of Busemann points. As…

Recent progress in multilinear harmonic analysis naturally raises questions about the local behaviour of the best constant (or bound) in the general Brascamp--Lieb inequality as a function of the underlying linear transformations. In this…

We establish a fixed point property for a certain class of locally compact groups, including almost connected Lie groups and compact groups of finite abelian width, which act by simplicial isometries on finite rank buildings with measurable…