Related papers: Structure of weighted Hardy spaces in the plane
We prove that the pointwise product of two holomorphic functions of the upper half-plane, one in the Hardy space $\mathcal H^1$, the other one in its dual, belongs to a Hardy type space. Conversely, every holomorphic function in this space…
The purpose of this article is to give another molecular decomposition for members of the weighted Hardy spaces.
We present a natural family of Hilbert function spaces on the d-dimensional complex unit ball and classify which of them satisfy that subsets of the ball yield isometrically isomorphic subspaces if and only if there is an analytic…
We prove that a conformal mapping defined on the unit disk belongs to a weighted Bergman space if and only if certain integrals involving the harmonic measure converge. With the aid of this theorem, we give a geometric characterization of…
On a homogeneous group, we characterize the one-parameter groups of dilations whose associated Hardy spaces in the sense of Folland and Stein are the same.
In this paper we study the bicomplex version of weighted Hardy spaces. Further, we describe reproducing kernels for the bicomplex weighted Hardy spaces. In particular, we generalize some results which holds for the classical weighted Hardy…
In this note we give several characterisations of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the…
We introduce noncommutative weak Orlicz spaces associated with a weight and study their properties. We also define noncommutative weak Orlicz-Hardy spaces and characterize their dual spaces.
In this paper, we completely characterize the order boundedness of weighted composition operators between different weighted Dirichlet spaces and different derivative Hardy spaces.
We define and prove characterizations of Hardy-Orlicz spaces of conformal densities.
In this paper we completely characterize those weighted Hardy spaces that are Poletsky--Stessin Hardy spaces $H^p_u$. We also provide a reduction of $H^\infty$ problems to $H^p_u$ problems and demonstrate how such a reduction can be used to…
It is proved that, under certain restrictions on weights, a pair of weighted Hardy spaces on the two-dimensional torus is K-closed in the pair of the corresponding weighted Lebesgue spaces. By now, K-closedness of Hardy spaces on the…
Characterizations of the associated spaces and second associated spaces of the Hardy space on $\mathbb{R}^n$ are given. Some results on the associated spaces of the $\textrm{BMO}(\mathbb{R}^n)$ space are proved also.
We study boundary uniqueness properties of Hardy space functions in several complex variables. Along the way, we develop properties of the Lumer Hardy space.
It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as…
We give a numerical characterization of weighted hyperplane arrangements arising from Dunkl systems.
In this paper, we introduce a discrete analogue of weighted Hardy spaces on rooted trees and study weighted composition operators between them in detail. In particular, we characterize bounded and compact weighted composition operators…
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 mainly discuss three things. First, there is no canonical norm on the space $H^p_u(\mathbb{D})$. Second, we improve the weak-$*$ convergence of the measures $\mu_{u,r}$. Third, the dilations $f_t$ of the function $f\in…
It is known that product singular integrals are bounded on product Hardy spaces and that flag singular integrals are bounded on flag Hardy spaces. The purpose of this paper is to obtain the complete boundedness of singular integrals on…