Related papers: Uniqueness Properties of Hardy Space Functions

In this paper, we are devoted to studying some sharp bounds for Hardy type operators on mixed radial-angular type function spaces. In addition, we will establish the sharp weak-type estimates for the fractional Hardy operator and its…

In this paper, the concept of grand variable Herz-Morrey-Hardy spaces are introduced. We also establish the atomic characterization of these spaces. As an application the authors investigate the continuity of a few singular integral…

In this paper, the authors define the weak Herz spaces and the weak Herz-type Hardy spaces with variable exponent. As applications, the authors establish the boundedness for a large class of singular integral operators including some…

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 review the literature concerning the Hardy inequality for regions in Euclidean space and in manifolds, concentrating on the best constants. We also give applications of these inequalities to boundary decay and spectral approximation.

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 the present paper we shall establish n-dimensional Hardy's inequalities with non-doubling weight functions of the distance to the boundary, where the boundary is a $C^2$ class bounded domain of $R^N$. This work is essentially based on…

We establish simple pointwise characterizations of functions in the Hardy-Sobolev spaces within the range n/(n+1)<p <=1. In addition, classical Hardy inequalities are extended to the case p <= 1.

This paper is devoted to Hardy type inequalities with remainders for compactly supported smooth functions on open sets in the Euclidean space. We establish new inequalities with weight functions depending on the distance function to the…

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 establish a characterization of the Hardy spaces on the homogeneous groups in terms of the Littlewood-Paley functions. The proof is based on vector-valued inequalities shown by applying the Peetre maximal function.

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 completely describe the boundedness of the Volterra type operator $J_ g$ between Hardy spaces in the unit ball of $\Cn$. The proof of the one dimensional case used tools, such as the strong factorization for Hardy spaces, that are not…

We prove certain generalization of Hardy's inequality where the "boundary defining function" is replaced by a polynomial defining a singular algebraic variety. An application is given on the existence of a small time heat trace expansion…

Boundary value problems for non-linear parabolic equations with singular potentials are considered. Existence and non-existence results as an application of different Hardy inequalities are proved. Blow-up conditions are investigated too.

We obtain new uniqueness theorems for harmonic functions defined on the unit disc or in the half plane. These results are applied to obtain new resolvent descriptions of spectral subspaces of polynomially bounded groups of operators on…

We define the Hardy spaces of free noncommutative functions on the noncommutative polydisc and the noncommutative ball and study their basic properties. Our technique combines the general methods of noncommutative function theory and…

We investigate the continuity and differentiability of the Hardy constant with respect to perturbations of the domain in the case where the problem involves the distance from a boundary submanifold. We also investigate the case where only…

We prove various representations and density results for Hardy spaces of holomorphic functions for two classes of bounded domains in $\mathbb C^n$, whose boundaries satisfy minimal regularity conditions (namely the classes $C^2$ and…

We develop the theory of variable exponent Hardy spaces. Analogous to the classical theory, we give equivalent definitions in terms of maximal operators. We also show that distributions in these spaces have an atomic decomposition including…