Related papers: Hardy spaces and dilations on homogeneous groups

Group lattices (Cayley digraphs) of a discrete group are in natural correspondence with differential calculi on the group. On such a differential calculus geometric structures can be introduced following general recipes of noncommutative…

We detect Hilbert manifolds among isometrically homogeneous metric spaces and apply the obtained results to recognizing Hilbert manifolds among homogeneous spaces of the form G/H where G is a metrizable topological group and H is a closed…

This paper obtains new characterizations of weighted Hardy spaces and certain weighted $BMO$ type spaces via the boundedness of variation operators associated with approximate identities and their commutators, respectively.

In this paper, we introduce a kind of homology which we call Hawaiian homology to study and classify pointed topological spaces. The Hawaiian homology group has advantages of Hawaiian groups. Moreover, the first Hawaiian homology group is…

Let $\mathbb{H}^{n}$ be the Heisenberg group and $Q = 2n+2$. For $1 < q < \infty$, $\gamma > 0$ and an exponent function $p(\cdot)$ on $\mathbb{H}^n$, which satisfy log-H\"older conditions, with $0 < p_{-} \leq p_{+} < \infty$, we introduce…

An algebraic variety $X$ is called a homogeneous space if there exists a transitive regular action of an algebraic group on $X$. We prove inequalities between the dimension of a homogeneous space of a linear algebraic group and its Picard…

We classify measures on a homogeneous space which are invariant under a certain solvable subgroup and ergodic under its unipotent radical. Our treatment is independent of characteristic. As a result we get the first measure classification…

The aim of this note is to give the boundedness conditions for Hausdorff operators on Hardy spaces $H^{1}$ with the norm defined via $(1,q)$ atoms over homogeneous spaces of Lie groups with doubling property and to apply results we obtain…

In this paper, we consider the first order Hardy inequalities using simple equalities. This basic setting not only permits to derive quickly many well-known Hardy inequalities with optimal constants, but also supplies improved or new…

We study $\epsilon$-representations of discrete groups by unitary operators on a Hilbert space. We define the notion of Ulam stability of a group which loosely means that finite-dimensional $\epsilon$-represendations are uniformly close to…

Here, we classify Lie groups acting isometrically on compact Lorentz manifolds, and in particular we describe the geometric structure of compact homogeneous Lorentz manifolds.

We study the compact perturbations of an isometry on a separable Hilbert space and provide a complete characterization of when they are quasinormal. Based on that, we present a complete classification for a rank-one perturbation of a…

We investigate the structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group. We work with square integrable representations, and we show that they are those for which we can construct an…

Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy…

Consider homogeneous G/H and G/F, for an S-algebraic group G. A lattice {\Gamma} acts on the left strictly conservatively. The following rigidity results are obtained: morphisms, factors and joinings defined apriori only in the measurable…

In this article, we determine conditions on the parameters of a generalized convolution operator such that it belongs to the Hardy space and to the space of bounded analytic functions. Results obtained are new and their usefulness is…

We investigate the isolated points in the space of finitely generated groups. We give a workable characterization of isolated groups and study their hereditary properties. Various examples of groups are shown to yield isolated groups. We…

We study the Hardy type inequalities in the framework of equalities. We present equalities which immediately imply Hardy type inequalities by dropping the remainder term. Simultaneously we give a characterization of the class of functions…

We consider the holomorphic unramified mapping of two arbitrary finite bordered Riemann surfaces. Extending the map to the doubles $X_1$ and $X_2$ of Riemann surfaces we define the vector bundle on the second double as a direct image of the…

We consider the products of composition and differentiation operators on the Hardy space. We provide a complete characterization of the boundedness and compactness of these operators. Furthermore, we obtain the explicit condition for these…