Related papers: On operator valued Hardy spaces

In this paper, we investigate various square functions on the complex unit ball. We prove the weighted inequalities of the Lusin area integral associated with Poisson integral in terms of $A_p$ weights for all $1<p<\infty$; this gives an…

Some special Hilbert spaces are introduced to present the class of infinitesimal operators with complete minimal non-basis family of eigenvectors. The discrete Hardy inequality plays an important role in the proposed approach. The…

Let $X$ be a space of homogeneous type and let $L$ be a sectorial operator with bounded holomorphic functional calculus on $L^2(X)$. We assume that the semigroup $\{e^{-tL}\}_{t>0}$ satisfies Davies-Gaffney estimates. Associated to $L$ are…

Fix $\lambda>0$. Consider the Hardy space $H^1(\mathbb{R}_+,dm_\lambda)$ in the sense of Coifman and Weiss, where $\mathbb{R_+}:=(0,\infty)$ and $dm_\lambda:=x^{2\lambda}dx$ with $dx$ the Lebesgue measure. Also consider the Bessel operators…

We prove the strong continuity of spectral multiplier operators associated with dilations of certain functions on the general Hardy space $H^1_L$ introduced by Hofmann, Lu, Mitrea, Mitrea, Yan. Our results include the heat and Poisson…

Let $L:=-\Delta+V$ be the Schr\"{o}dinger operator on $\mathbb{R}^n$ with $n\geq 3$, where $V$ is a non-negative potential which belongs to certain reverse H\"{o}lder class $RH_q(\mathbb{R}^n)$ with $q\in (n/2,\,\infty)$. In this article,…

We first consider two types of localizations of singular integral operators of convolution type, and show, under mild decay and smoothness conditions on the auxiliary functions, that their boundedness on the local Hardy space…

In this work, we prove that weak compactness of composition operator on $H^{1}(U^{n})$ coincides with its compactness. We also characterize bounded and compact composition operators on $H^{1}(U^{n}).$\

We study mapping properties of the centered Hardy--Littlewood maximal operator $\mathcal{M}$ acting on Lorentz spaces $L^{p,q}(\mathfrak{X})$ in the context of certain non-doubling metric measure spaces $\mathfrak{X}$. The special class of…

In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of…

Let ${\mathfrak A}$ be a $C^*$-algebra, $T$ be a locally compact Hausdorff space equipped with a probability measure $P$ and let $(A_t)_{t\in T}$ be a continuous field of operators in ${\mathfrak A}$ such that the function $t \mapsto A_t$…

Let $\vec{p}\in(0,\infty)^n$ and $A$ be a general expansive matrix on $\mathbb{R}^n$. In this article, via the non-tangential grand maximal function, the authors first introduce the anisotropic mixed-norm Hardy spaces…

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…

Boundedness of an abstract formulation of Hardy operators between Lebesgue spaces over general measure spaces is studied and, when the domain is L^1, shown to be equivalent to the existence of a Hardy inequality on the half line with…

In this paper a reduction and equivalence theorems for the boundedness of the composition of a quasilinear operator $T$ with the Hardy and Copson operators in weighted Lebesgue spaces are proved. New equivalence theorems are obtained for…

By a theorem of Bayart, $\varphi$ generates a bounded composition operator on the Hardy space $\Hp$of Dirichlet series ($1\le p<\infty$) only if $\varphi(s)=c_0 s+\psi(s)$, where $c_0$ is a nonnegative integer and $\psi$ a Dirichlet series…

Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$ and $H_X({\mathbb R}^n)$ the Hardy space associated with $X$, and let $\alpha\in(0,n)$ and $\beta\in(1,\infty)$. In this article, assuming that the (powered) Hardy--Littlewood…

We introduce a variable exponent version of the Hardy space of analytic functions on the unit disk, we show some properties of the space, and give an example of a variable exponent $p(\cdot)$ that satisfies the $\log$-H\"older condition…

For a Dirichlet series symbol $g(s) = \sum_{n \geq 1} b_n n^{-s}$, the associated Volterra operator $\mathbf{T}_g$ acting on a Dirichlet series $f(s)=\sum_{n\ge 1} a_n n^{-s}$ is defined by the integral $f\mapsto -\int_{s}^{+\infty}…

For $g \in \operatorname{Hol}(\mathbb D)$, we study the class of generalized integration operators $T_{g,a}$, acting on Hardy and Bergman spaces of the unit disc in the complex plane. This class of integral operators were introduced to…