Related papers: Hardy spaces and dilations on homogeneous groups

The concept of space group has long served as the fundamental framework to describe the physical properties of crystalline materials, from electronic bands to photonic dispersions. The recent progress of spatiotemporal control, such as…

A function which is analytic and bounded in the Unit disk is called a generator for the Hardy space or the Bergman space if polynomials in that function are dense in the corresponding space. We characterize generators in terms of sub-spaces…

Let (M, g) be a complete Riemannian manifold. Assume that the Ricci curvature of M has quadratic decay and that the volume growth is strictly faster than quadratic. We establish that the Hardy spaces of exact 1-differential forms on M ,…

We study actions of finite groups on moduli spaces of stable holomorphic vector bundles and relate the fixed-point sets of those actions to representation varieties of certain orbifold fundamental groups.

The Hardy spaces are defined on the quotient domain of a bounded complete Reinhardt domain by a finite subgroup of $U(n)$. The Szeg\H{o} projection on the quotient domain can be studied by lifting to the covering space. This setting builds…

We develop the foundations of the deformation theory of compact complete affine space forms and affine crystallographic groups. Using methods from the theory of linear algebraic groups we show that these deformation spaces inherit an…

In this paper we give a characterization of the possible homology groups that can occur for compact simply connected cohomogeneity one manifolds in dimensions seven and lower.

We consider an infinite homogeneous tree V endowed with the usual metric d defined on graphs and a weighted measure \mu. The metric measure space V,d,\mu) is nondoubling and of exponential growth, hence the classical theory of Hardy spaces…

The aim of this paper is to characterize in broad classes of means the so-called Hardy means, i.e., those means $M\colon\bigcup_{n=1}^\infty \mathbb{R}_+^n\to\mathbb{R}_+$ that satisfy the inequality $$ \sum_{n=1}^\infty M(x_1,\dots,x_n)…

Let $G$ be a complex reductive connected algebraic group equipped with the Sklyanin bracket. A classification of Poisson homogeneous $G$-spaces with connected isotropy subgroups is given. This result is based on Drinfeld's correspondence…

In this paper, carrying on with our study of the Hardy-amalgam spaces $\mathcal H^{(q,p)}$ and $\mathcal{H}_{\mathrm{loc}}^{(q,p)}$ ($0<q,p<+\infty$), we give a characterization of their duals whenever $0<q\leq 1<p<+\infty$. Moreover, when…

Coarse geometry is the study of large-scale properties of spaces. In this paper we study group coarse structures (i.e., coarse structures on groups that agree with the algebraic structures), by using group ideals. We introduce a large class…

We characterize invariant subspaces of Brownian shifts on vector-valued Hardy spaces. We also solve the unitary equivalence problem for the invariant subspaces of these shifts.

In this work, we introduce Orlicz-Hardy type spaces and Orlicz-Calder\'on Hardy type spaces on the Heisenberg group $\mathbb{H}^{n}$ and study the relationship between them by means of the Heisenberg sub-Laplacian $\mathcal{L}$. More…

This paper defines local weighted Hardy spaces with variable exponent. Local Hardy spaces permit atomic decomposition, which is one of the main themes in this paper. A consequence is that the atomic decomposition is obtained for the…

We exhibit a family of homogeneous hypersurfaces in affine space, one in each dimension, generalising the Cayley surface.

Permutation products and their various "fat diagonal" subspaces are studied from the topological and geometric point of view. We describe in detail the stabilizer and orbit stratifications related to the permutation action, producing a…

We investigate the Hardy space $H^1_L$ associated with a self-adjoint operator $L$ defined in a general setting in [S. Hofmann, et. al., Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates,…

We classify surface Houghton groups, as well as their pure subgroups, up to isomorphism, commensurability, and quasi-isometry.

We organize fundamental properties of quasi-Hamiltonian spaces on which a finite group acts, and we apply them to the theory of moduli spaces of flat connections on an oriented compact surface with boundary.