Related papers: Martingale transform and L\'evy Processes on Lie G…

The main purpose of this paper is to prove H\"ormander's $L^p$-$L^q$ boundedness of Fourier multipliers on commutative hypergroups. We carry out this objective by establishing Paley inequality and Hausdorff-Young-Paley inequality for…

We construct optimal Markov couplings of L\'{e}vy processes, whose L\'evy (jump) measure has an absolutely continuous component. The construction is based on properties of subordinate Brownian motions and the coupling of Brownian motions by…

Bourgain in his seminal paper [2] about the analysis of maximal functions associated to convex bodies, has estimated in a sharp way the $L^2$-operator norm of the maximal function associated to a kernel $K\in L^1,$ with differentiable…

In this note we extend to metrizable profinite groups the classical theorems of Titchmarsh on the Fourier transform of H\"older-Lipschitz functions. This generalizes the results of Younis on compact zero-dimensional abelian groups to the…

The aim of this work is to extend and study a family of transformations between Laplace exponents of L\'evy processes which have been introduced recently in a variety of different contexts by Patie, Kyprianou and Patie, and, Gnedin, as well…

We give several sharp estimates for a class of combinations of second order Riesz transforms on Lie groups ${G}={G}_{x} \times {G}_{y}$ that are multiply connected, composed of a discrete abelian component ${G}_{x}$ and a connected…

Complete sets of bases of differential invariants, operators of invariant differentiation and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of…

A random Lie group action on a compact manifold generates a discrete time Markov process. The main object of this paper is the evaluation of associated Birkhoff sums in a regime of weak, but sufficiently effective coupling of the…

In this paper, from the viewpoint of the concentration theory of maps, we study a compact group and a L\'{e}vy group action to a large class of metric spaces, such as R-trees, doubling spaces, metric graphs, and Hadamard manifolds.

We show that on groups generated by bounded activity automata, every symmetric, finitely supported probability measure has the Liouville property. More generally we show this for every group of automorphisms of bounded type of a rooted…

We consider a class of L\'evy-type processes on which spectral analysis technics can be made to produce optimal results, in particular for the decay rate of their survival probability and for the spectral gap of their ground state…

The purpose of this paper is to develop a deformation theory controlled by pre-Lie algebras with divided powers over a ring of positive characteristic. We show that every differential graded pre-Lie algebra with divided powers comes with…

We calculate the norm of the Fourier operator from $L^p(X)$ to $L^q(\hat{X})$ when $X$ is an infinite locally compact abelian group that is, furthermore, compact or discrete. This subsumes the sharp Hausdorff-Young inequality on such…

We start by defining a subordinator by means of the lower-incomplete gamma function. It can be considered as an approximation of the stable subordinator, easier to be handled thank to its finite activity. A tempered version is also…

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…

We present a discrete analog of the recently introduced Hamilton-Pontryagin variational principle in Lagrangian mechanics. This unifies two, previously disparate approaches to discrete Lagrangian mechanics: either using the discrete…

Let $G$ be a locally compact Abelian group with a fixed Haar measure and, denote by $\widehat{G}$ its dual group. In this article, the authors obtain various boundedness of the short-time Fourier transform on Lorentz spaces:…

In [16], under mild conditions, a Wiener-Hopf type factorization is derived for the exponential functional of proper L\'evy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by…

Given a Lie group $G$ of quantized canonical transformations acting on the space $L^2(M)$ over a closed manifold $M$, we define an algebra of so-called $G$-operators on $L^2(M)$. We show that to $G$-operators we can associate symbols in…

Sets of orthogonal martingales are importants because they can be used as stochastic integrators in a kind of chaotic representation property, see [20]. In this paper, we revisited the problem studied by W. Schoutens in [21], investigating…