Related papers: Paley's inequality for nonabelian groups
A classical result due to Paley and Wiener characterizes the existence of a non-zero function in $L^2(\mathbb{R})$, supported on a half line, in terms of the decay of its Fourier transform. In this paper we prove an analogue of this result…
In this work we define operator-valued Fourier transforms for suitable integrable elements with respect to the Plancherel weight of a (not necessarily Abelian) locally compact group. Our main result is a generalized version of the Fourier…
We modify the standard proof of Paley's theorem about lacunary coefficients of functions in $H^1$ to work without analytic factorization. This leads to the first direct proof of the extension of Paley's theorem that we applied to the former…
In the article "Picard-Vessiot theory of differentially simple rings" we established a Picard-Vessiot theory over differentially simple rings which may not be fields. Differential modules over such rings were proven to be locally free but…
We consider the fractional derivative of a general Poisson semigroup. With this fractional derivative we define the generalized fractional Littlewood-Paley $g$-function for semigroups acting on $L^p$-spaces of functions with values in…
We provide a general scheme for proving $L^p$ estimates for certain bilinear Fourier restrictions outside the locally $L^2$ setting. As an application, we show how such estimates follow for the lacunary polygon. In contrast with prior…
Extending pioneering work by Weinberg, Conrad, McCleary, and others, we provide a systematic way of relating spaces of right orders on a partially ordered group, on the one hand, and spectral spaces of free lattice-ordered groups, on the…
A version of Paley-Wiener like theorem for connected, simply connected nilpotent Lie groups is proven.
We observe that classical arguments of Ricci--Stein can be used to prove $L^p$ bounds for maximal functions associated to lacunary dilates of a fixed measure in the setting of homogenous groups. This recovers some recent results on averages…
In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second…
The one-sided Littlewood--Paley inequality for arbitrary intervals was proved by Rubio de Francia. Later, N. Osipov proved its analogue for the system of Walsh functions. In this paper, this inequality is proved for more general Vilenkin…
This paper deals with the Langlands' classification for discrete series of unitary quasi-split p-adic groups. We show that such a classification follows from Arthur's work on the simple trace formula which we can use now thanks to…
This article focuses on the study of zero-sum invariants of finite non-abelian groups. We address two main problems: the first centers on the ordered Davenport constant and the second on Gao's constant. We establish a connection between the…
The paper studies short exact sequences of Banach modules over the convolution algebra $L_1=L_1(G)$, where $G$ is a compact abelian group. The main tool is the notion of a nonlinear $L_1$-centralizer, which in combination with the Fourier…
Following the works of Lyons and Oberlin, Seeger, Tao, Thiele and Wright, we relate the variation of certain discrete curves on the Lie group $\text{SU}(1,1)$ to the corresponding variation of their linearized versions on the Lie algebra.…
A version of Littlewood-Paley-Rubio de Francia inequality for bounded multi-parameter Vilenkin systems is proved: for any family of disjoint sets $I_k = I_k^1 \times \ldots \times I_k^D \subseteq {\mathbb{Z}_+^D}$ such that $I_k^d$ are…
We extend the Ruzhansky-Turunen theory of pseudo differential operators on compact Lie groups into a tool that can be used to investigate group-valued Markov processes in the spirit of the work in Euclidean spaces of N.Jacob and…
The classification of gradings by abelian groups on finite direct sums of simple finite-dimensional nonassociative algebras over an algebraically closed field is reduced, by means of the use of loop algebras, to the corresponding problem…
In this paper we study the existence of free non-abelian subgroups in non-central permutable subgroups of general skew linear groups and locally finite group algebras.
This paper focuses on the fractional difference of Lyapunov functions related to Riemann-Liouville, Caputo and Grunwald-Letnikov definitions. A new way of building Lyapunov functions is introduced and then five inequalities are derived for…