Related papers: Uniqueness Properties of Hardy Space Functions

Let $L= - \mathrm{div} (A \nabla \cdot)$ be an elliptic operator defined on an open subset of $\mathbb{R}^d$, complemented with mixed boundary conditions. Under suitable assumptions on the operator and the geometry, we derive an atomic…

We obtain sharp Hardy inequalities on antisymmetric functions where antisymmetry is understood for multi-dimensional particles. Partially it is an extension of the previously published paper \cite{HL}, where Hardy's inequalities were…

We study boundary properties of plurisubharmonic functions near real submanifolds of almost complex manifolds.

We present recent results on elliptic boundary value problems where the theory of Hardy spaces associated with operators plays a key role.

We establish exact conditions for non triviality of all subspaces of the standard Hardy space in the upper half plane, that consist of character automorphic functions with respect to the action of a discrete subgroup of $SL_2(\mathbb R)$.…

It is a classical theorem that if a function is integrable along the boundary of the unit circle, then the function is the nontangential limit of a holomorphic function on the open disc if and only if its Fourier coefficients for…

We introduce generalized Fofana spaces and we give some of their basic properties. These spaces are a kind of generalization of generalized Morrey spaces. As application, we establish the boundedness of the Hardy-Littlewood maximal operator…

The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…

We study some approximation problems on a strict subset of the circle by analytic functions of the Hardy space H2 of the unit disk (in C), whose modulus satisfy a pointwise constraint on the complentary part of the circle. Existence and…

We study some Hardy-type inequalities involving a general norm in $R^n$ and an anisotropic distance function to the boundary. The case of the optimality of the constants is also addressed.

This paper is devoted to Hardy inequalities concerning distance functions from submanifolds of arbitrary codimensions in the Riemannian setting. On a Riemannian manifold with non-negative curvature, we establish several sharp weighted Hardy…

This work establishes a strong uniqueness property for a class of planar locally integrable vector fields. A result on pointwise convergence to the boundary value is also proved for bounded solutions.

We prove sharp local and global variation bounds for the centred Hardy--Littlewood maximal functions of indicator functions in one dimension. We characterise maximisers, treat both the continuous and discrete settings and extend our results…

We characterize conditional Hardy spaces of the Laplacian and of the fractional Laplacian by using Hardy-Stein type identities.

In this paper, we will study the boundedness properties of multilinear Calderon--Zygmund operators and multilinear fractional integrals on products of weighted Morrey spaces with multiple weights.

We obtain boundedness from a product of Lebesgue or Hardy spaces into Hardy spaces under suitable cancellation conditions for a large class of multilinear operators that includes the Coifman-Meyer class, sums of products of linear…

In this article, we further explore convex functions by revealing new bounds, resulting from stronger convexity behavior. In particular, we define the so called radical convex functions and study their properties. We will see that such…

In this paper, we prove the boundedness of multilinear fractional integral operators from products of Hardy spaces associated with ball quasi-Banach function spaces into their corresponding ball quasi-Banach function spaces. As…

For smoothly bounded, strongly $\mathbb{C}$-convex domains, one can use the Fefferman form or its variants to define projectively invariant norms on sections of holomorphic line bundles, producing a Hardy space. In two variables, we…

We study Hardy spaces for Fourier--Bessel expansions associated with Bessel operators on $((0,1), x^{2\nu+1}\, dx)$ and $((0,1), dx)$. We define Hardy spaces $H^1$ as the sets of $L^1$-functions for which their maximal functions for the…