Related papers: Hardy classes, integral operators, and duality on …

We consider several differential operators on compact almost-complex, almost-Hermitian and almost-K\"ahler manifolds. We discuss Hodge Theory for these operators and a possible cohomological interpretation. We compare the associated spaces…

This paper is devoted to the study of semigroups of composition operators and semigroups of holomorphic mappings. We establish conditions under which these semigroups can be extended in their parameter to sector given a priori. We show that…

We introduce the class of variable anisotropic singular integral operators associated to a continuous multi-level ellipsoid cover $\Theta$ of $\mathbb{R}^n$ introduced by Dahmen, Dekel, and Petrushev \cite{ddp}. This is an extension of the…

We study Hardy spaces associated with a general multidimensional Bessel operator $\mathbb{B}_\nu$. This operator depends on a multiparameter of type $\nu$ that is usually restricted to a product of half-lines. Here we deal with the Bessel…

In this paper, we investigate the two-weight Hardy inequalities on metric measure space possessing polar decompositions for the case $p=1$ and $1 \leq q <\infty.$ This result complements the Hardy inequalities obtained in \cite{RV} in the…

In this article, we give a short proof of Hardy's inequality for Hermite expansions of functions in the classical Hardy spaces $H^p({\mathbb R^n})$, by using an atomic decomposition of the Hardy spaces associated with the Hermite operators.…

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…

In this paper, we introduce homogeneous mixed Herz-Morrey spaces $M\dot{K}_{p,\vec{q}}^{\alpha,\lambda}(\mathbb{R}^n)$ and show it's some properties. Firstly, the boundedness of sublinear operators, fractional type operators in homogeneous…

The Hardy spaces for Fourier integral operators $\mathcal{H}_{FIO}^{p}(\mathbb{R}^{n})$, for $1\leq p\leq \infty$, were introduced by Smith in [Smith,1998] and Hassell et al. in [Hassell-Portal-Rozendaal,2020]. In this article, we give…

We completely characterize the boundedness of the Volterra type integration operators $J_b$ acting from the weighted Bergman spaces $A^p_\alpha$ to the Hardy spaces $H^q$ of the unit ball of $\mathbb{C}^n$ for all $0<p,q<\infty$. A partial…

Let $\Omega$ be a strongly Lipschitz domain of $\reel^n$. Consider an elliptic second order divergence operator $L$ (including a boundary condition on $\partial\Omega$) and define a Hardy space by imposing the non-tangential maximal…

In this paper, we consider the first order Hardy inequalities using simple equalities. This basic setting not only permits to derive quickly many well-known Hardy inequalities with optimal constants, but also supplies improved or new…

We do research on the real method of Hardy spaces associated with the Dunkl setting on the real line for the range of 0<p<=1.

We define local Hardy spaces of differential forms $h^p_{\mathcal D}(\wedge T^*M)$ for all $p\in[1,\infty]$ that are adapted to a class of first order differential operators $\mathcal D$ on a complete Riemannian manifold $M$ with at most…

Let $\Gamma$ be a Lipschitz curve on the complex plane $\mathbb{C}$ and $\Omega_+$ is the domain above $\Gamma$, we define Hardy space $H^p(\Omega_+)$ as the set of holomorphic functions $F$ satisfying $\sup_{\tau>0}(\int_{\Gamma}…

Let X be a noncompact symmetric space of rank one and let h^1(X) be a local atomic Hardy space. We prove the boundedness from h^1(X) to L^1(X) and on h^1(X) of some classes of Fourier integral operators related to the wave equation…

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

We study the behaviour of Hardy-weights for a class of variational quasi-linear elliptic operators of $p$-Laplacian type. In particular, we obtain necessary sharp decay conditions at infinity on the Hardy-weights in terms of their…

We complete the different cases remaining in the estimation of the essential norm of a weighted composition operator acting between the Hardy spaces $H^p$ and $H^q$ for $1\leq p,q\leq\infty.$ In particular we give some estimates for the…

In this paper, we investigate when weighted composition operators acting on Dirichlet spaces $\mathcal{D}(\mathbb{B}_{N})$ are complex symmetric with respect to some special conjugations, and provide some characterizations of Hermitian…