Related papers: Analytic Variable Exponent Hardy Spaces

We study estimates for Hardy space norms of analytic projections. We first find a sufficient condition for the Bergman projection of a function in the unit disc to belong to the Hardy space $H^p$ for $1 < p < \infty$. We apply the result to…

Let $\A$ be a finite subdiagonal algebra in Arveson's sense. Let $H^p(\A)$ be the associated noncommutative Hardy spaces, $0<p\le\8$. We extend to the case of all positive indices most recent results about these spaces, which include…

Maximal and atomic Hardy spaces Hp and HAp , are considered in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. It is…

It is proved an inequality - integrated analogue of the Hardy inequality and as application simplified proof of the theorem of S. A. Vinogradov for the bounded Toeplitz operators on the space of functions analytic and bounded in the unit…

In this paper we introduce variable exponent local Hardy spaces associated with a non-negative self-adjoint operator L. We define them by using an area square integral involving the heat semigroup associated to L. A molecular…

In this note we continue giving the characterisation of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the…

It is studied that pointwise estimates and continuities on Hardy spaces of pseudo-differential operators (PDOs for short) with the symbol in general H\"{o}rmander's classes. We get weighted weak-type $(1,1)$ estimate, weighted normal…

We define new generalized Herz spaces having weight and variable exponent, that is, weighted Herz spaces with variable exponent. We prove the boundedness of an intrinsic square function on those spaces under proper assumptions on each…

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.

In this paper, the fractional Hardy-type operator of variable order $\beta(x)$ is shown to be bounded from the variable exponent Herz-Morrey spaces $M\dot{K}_{p_{_{1}},q_{_{1}}(\cdot)}^{\alpha(\cdot),\lambda}(\R^{n})$ into the weighted…

We investigate Hardy spaces $H^1_L(X)$ corresponding to self-adjoint operators $L$. Our main aim is to obtain a description of $H^1_L(X)$ in terms of atomic decompositions similar to such characterisation of the classical Hardy spaces…

The Hardy spaces of Dirichlet series denoted by ${\cal H}^p$ ($p\ge1$) have been studied in [12] when p = 2 and in [3] for the general case. In this paper we study some Lp-generalizations of spaces of Dirichlet series, particularly two…

In this paper, carrying on with our study of the Hardy-amalgam spaces $\mathcal H^{(q,p)}$ and $\mathcal{H}_{\mathrm{loc}}^{(q,p)}$ ($0<q,p<+\infty$), we give a characterization of their duals whenever $0<q\leq 1<p<+\infty$. Moreover, when…

In this article, we establish sharp weak endpoint estimates for $p$-adic fractional Hardy operator. In addition, sharp weak bounds for p-adic Hardy operator on p-adic central Morrey space are also obtained.

Let $\vec{a}:=(a_1,\ldots,a_n)\in[1,\infty)^n$, $\vec{p}:=(p_1,\ldots,p_n)\in(0,\infty)^n$ and $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$ be the anisotropic mixed-norm Hardy space associated with $\vec{a}$ defined via the non-tangential grand…

We obtain a new square function characterization of the weak Hardy space $H^{p,\infty}$ for all $p\in(0,\iy)$. This space consists of all tempered distributions whose smooth maximal function lies in weak $L^p$. Our proof is based on…

It is well known that if Hardy-Littlewood maximal operator is bounded in space $L^{p(\cdot)}[0;1]$ then $1/p(\cdot)\in BMO^{1/\log}$. On the other hand if $p(\cdot)\in BMO^{1/\log},$ ($1<p_{-}\leq p_{+}<\infty$), then there exists $c>0$…

This paper establishes existence of solutions for a partial differential equation in which a differential operator involving variable exponent growth conditions is present. This operator represents a generalization of the $p(\cdot)$-Laplace…

Title: On linear extension for interpolating sequences. Author: Eric Amar Abstract: Let A be a uniform algebra on the compact space X and $\sigma $ a probability measure on X. We define the Hardy spaces $H^{p}(\sigma)$ and the…

We characterize the sufficient conditions which three weight functions $u$ and $v_{1}, v_{2}$ satisfy ensure the boundedness of the Hardy operator with variable limits on product space. The corresponding bound is explicitly worked out.…