Related papers: Uniqueness Properties of Hardy Space Functions

This paper provides a study of problems related to Hardy spaces left by G.\,Weiss in \cite{We}. First, We will prove that the Hardy spaces $H^p(\mathbb{R}^n)$ can be characterized by a fixed Lipschitz function.

Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…

We study Hardy type inequalities involving mixed cylindrical and spherical weights, for functions supported in cones. These inequalities are related to some singular or degenerate differential operators.

In this paper, by using the atomic decomposition theory of weighted Hardy spaces, we will give some weighted weak type estimates for intrinsic square functions including the Lusin area function, Littlewood-Paley $g$-function and…

We prove sharp homogeneous improvements to $L^1$ weighted Hardy inequalities involving distance from the boundary. In the case of a smooth domain, we obtain lower and upper estimates for the best constant of the remainder term. These…

We study Hardy spaces of solutions to the conjugate Beltrami equation with Lipschitz coefficient on Dini-smooth simply connected planar domains, in the range of exponents $1<\infty$. We analyse their boundary behaviour and certain density…

In this paper, we will study the boundedness properties of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_\lambda$-function on the weighted Morrey spaces $L^{p,\kappa}(w)$ for…

We study the Hardy identities and inequalities on Cartan-Hadamard manifolds using the notion of a Bessel pair. These Hardy identities offer significantly more information on the existence/nonexistence of the extremal functions of the Hardy…

In this research notes, we investigate some remain problems in the uniqueness of meromorphic function. Using some deep results of Yamanoii, we obtain some results in this notes.

Using Carleman estimates, we give a lower bound for solutions to the discrete Schr\"odinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of the solutions.

This paper is concerned with the applications of local features of the quaternion Hardy function. The feature information can be provided by the polar form of the quaternion Hardy function, such as the local attenuation and local phase…

We give a new characterization of character-automorphic Hardy spaces of order 2 and of their contractive multipliers in terms of de Branges Rovnyak spaces. Keys tools in our arguments are analytic extension and a factorization result for…

The consrtuction of self-similar fuctions in $L_2[0,1]$ is described. Some properties of such funtions (boundness of variation, continuity etc.) is obtained.

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.

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.

With the help of a radially invariant vector field, we derive inequalities of the Hardy kind, with no boundary terms, for $W^{1,p}$ functions on bounded star domains. Our results are not obtainable from the classical inequalities for…

We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.

In this paper we focus on various aspects of singular complex plane curves, mostly in the context of their homological properties and the associated combinatorial structures. We formulate some challenging open problems that can point to new…

Two-sided bounds for the efficiency of the torsion function are obtained in terms of the square of the distance to the boundary function under the hypothesis that the Dirichlet Laplacian satisfies a strong Hardy inequality. Localisation…

We study harmonic functions for the Laplace-Beltrami operator on the real hyperbolic ball. We obtain necessary and sufficient conditions for this functions and their normal derivatives to have a boundary distribution.In doing so, we put…