Related papers: On the multiplier problem for the ball on graded L…

Conditions for a function (number sequence) to be a multiplier on the space of integrable functions on $\Bbb R$ ($\Bbb T$) are given. This generalizes recent results of Giang and Moricz.

Let $G$ be a finite $p$-group and $N$ be a normal subgroup of $G$, with $|N|=p^n$ and $|G/N|=p^m$. A result of Ellis (1998) shows that the order of the Schur multiplier of such a pair $(G,N)$ of finite $p$-groups is bounded by $…

In this paper, we find an upper bound for the exponent of the Schur multiplier of a pair $(G,N)$ of finite $p$-groups, when $N$ admits a complement in $G$. As a consequence, we show that the exponent of the Schur multiplier of a pair…

In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or…

We study a parametrized family of strong maximal fractional operators. We prove their $L^p$ to $L^q$ boundedness for $1<p\le q<\infty$.

Classical pseudo-differential operators of order zero on a graded nilpotent Lie group $G$ form a $^*$-subalgebra of the bounded operators on $L^2(G)$. We show that its $C^*$-closure is an extension of a noncommutative algebra of principal…

In this paper we study the boundedness of global pseudo-differential operators on smooth manifolds. By using the notion of global symbol we extend a classical condition of H\"ormander type to guarantee the $L^p$-$L^q$-boundedness of global…

The aim of this article is to study the $L^{p}$-boundedness of pseudo-differential operators on a homogeneous tree $ \mathfrak{X} $. For $p\in (1,2)$, we establish a connection between the $L^{p}$-boundedness of the pseudo-differential…

In [24, Theorem 2'] Charles Fefferman has proved the weak (1,1) boundedness for a class of oscillating singular integrals that includes the oscillating spectral multipliers of the Euclidean Laplacian $\Delta,$ namely, operators of the form…

Let $G$ be the unramified unitary group $U(2, 1)(E/F)$ defined over a non-archimedean local field $F$ of odd residue characteristic $p$, and $B$ be the standard Borel subgroup of $G$. In this note, we study the problem of the restriction of…

We study solutions to the Brauer embedding problem with restricted ramification. Suppose $G$ and $A$ are a abelian groups, $E$ is a central extension of $G$ by $A$, and $f:\text{Gal}(\overline{\mathbf{Q}}/\mathbf{Q})\rightarrow G$ a…

We describe an algorithm for computing successive quotients of the Schur multiplier $M(G)$ for a group $G$ given by an invariant finite $L$-presentation. As application, we investigate the Schur multipliers of various self-similar groups…

Let $G=N\rtimes \mathbb{R}$, where $N$ is a Carnot group and $\mathbb{R}$ acts on $N$ via automorphic dilations. Homogeneous left-invariant sub-Laplacians on $N$ and $\mathbb{R}$ can be lifted to $G$, and their sum is a left-invariant…

We consider the problem whether for a group G there exists a constant Lambda(G) > 1 such that for any (r,s)-matrix A over the integral group ring ZG the Fuglede-Kadison determinant of the G-equivariant bounded operator from L^2(G)^r to…

We show that Riesz transforms associated to the Grushin operator G = -\Delta - |x|^2\partial_t^2 are bounded on L^p(R^n+1). We also establish an analogue of H\"ormander-Mihlin multiplier theorem and study Bochner-Riesz means associated to…

Consider a restriction of an irreducible finite dimensional holomorphic representation of $\GL(n+1,C)$ to the subgroup $GL(n,C)$ (it is determined by the Gelfand-Tsetlin branching rule). We write explicitly formulas for generators of the…

In this paper we investigate the $L^p$-boundedness of certain classes of periodic pseudo-differential operators. The operators considered arise from the study of symbols on $\mathbb{T}^n\times\mathbb{Z}^n$ with limited regularity.

Assuming the Generalized Riemann Hypothesis, we establish explicit bounds in the $q$-aspect for the logarithmic derivative $\left(L'/L\right)\left(\sigma,\chi\right)$ of Dirichlet $L$-functions, where $\chi$ is a primitive character modulo…

We classify self-adjoint first-order differential operators on weighted Bergman spaces on the $N$-dimensional unit ball $\mathbb{B}^N$ and $\mathbb{D}^2$ of $2\times2$ complex matrices satisfying $I-ZZ^*>0$.Our main tools are the discrete…

We establish regularity conditions for $L_p$-boundedness of Fourier multipliers on the group von Neumann algebras of higher rank simple Lie groups. This provides a natural H\"ormander-Mikhlin criterion in terms of Lie derivatives of the…