Related papers: Uniqueness Properties of Hardy Space Functions

This is a survey on rigidity and geometrization results obtained with the help of the discrete Hilbert-Einstein functional, written for the proceedings of the "Discrete Curvature" colloquium in Luminy.

We generalize the notion of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These conjugate functions are in general far from being…

We define and prove characterizations of Hardy-Orlicz spaces of conformal densities.

We pose some open problems related to boundedness of real-valued functions on balleans and coarse spaces. Also we prove that the Bergman property of groups is a coarse invariant. A special attention is payed to balleans on groups.

We consider the $L^p$ Hardy inequality involving the distance to the boundary for a domain in the $n$-dimensional Euclidean space. We study the dependence on $p$ of the corresponding best constant and we prove monotonicity, continuity and…

In this paper, we will discuss several radii problems related to Wright Function involving four parameters.

We consider the Hardy constant associated with a domain in the $n$-dimensional Euclidean space and we study its variation upon perturbation of the domain. We prove a Fr\'{e}chet differentiability result and establish a Hadamard-type formula…

For $1/2<p<1$, a description of inner functions whose derivative is in the Hardy space $H^p$ is given in terms of either their mapping properties or the geometric distribution of their zeros.

New Hardy type inequalities in sectorial area and as a limit in an exterior of a ball are proved. Sharpness of the inequalities is shown as well.

In this paper, we continue the development of a fundament of discrete octonionic analysis that is associated to the discrete first order Cauchy-Riemann operator acting on octonions. In particular, we establish a discrete octonionic version…

The goal of the present paper is to introduce and study noncommutative Hardy spaces associated with the regular $\Lambda$-polyball, to develop a functional calculus on noncommutative Hardy spaces for the completely non-coisometric (c.n.c.)…

We set a framework for the study of Hardy spaces inherited by complements of analytic hypersurfaces in domains with a prior Hardy space structure. The inherited structure is a filtration, various aspects of which are studied in specific…

We consider a class of weighted harmonic functions in the open upper half-plane known as $\alpha$-harmonic functions. Of particular interest is the uniqueness problem for such functions subject to a vanishing Dirichlet boundary value on the…

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…

In this work we prove some Hardy-Poincar\'{e} inequalities with quadratic singular potentials localized on the boundary of a smooth domain. Then, we consider conical domains with vertex on the singularity and we show upper and lower bounds…

We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.

This paper aims to obtain decompositions of higher dimensional $L^p(\mathbb{R}^n)$ functions into sums of non-tangential boundary limits of the corresponding Hardy space functions on tubes for the index range $0<p<1$. In the one-dimensional…

We establish endpoint bounds on a Hardy space $H^1$ for a natural class of multiparameter singular integral operators which do not decay away from the support of rectangular atoms. Hence the usual argument via a Journ\'e-type covering lemma…

In this paper, by using the decomposition theorem for weak Hardy spaces, we will obtain the boundedness properties of some integral operators with variable kernels on these spaces, under some Dini type conditions imposed on the variable…

In this article we study the strong unique continuation property for solutions of higher order (variable coefficient) fractional Schr\"odinger operators. We deduce the strong unique continuation property in the presence of subcritical and…