相关论文: Duality of certain Banach spaces of vector-valued …

In this article, we consider the following fractional {Hardy-type} inequality: \begin{align} \label{Fractional Hardy_abst} \int_{\mathbb{R}^N} |w(x)||u(x)|^p \mathrm{d}x \leq C \int_{\mathbb{R}^N \times \mathbb{R}^N}…

The concept of Rademacher type $p$ ($1\leq p\leq2$) plays an important role in the local theory of Banach spaces. In \cite{mas88} Mascioni considers a weakening of this concept and shows that for a Banach space $X$ weak Rademacher type $p$…

Let $L$ be a one-to-one operator of type $\omega$ in $L^2(\mathbb{R}^n)$, with $\omega\in[0,\,\pi/2)$, which has a bounded holomorphic functional calculus and satisfies the Davies-Gaffney estimates. Let $p(\cdot):\ \mathbb{R}^n\to(0,\,1]$…

Let $X$ and $Y$ be completely regular spaces and $E$ and $F$ be Hausdorff topological vector spaces. We call a linear map $T$ from a subspace of $C(X,E)$ into $C(Y,F)$ a \emph{Banach-Stone map} if it has the form $Tf(y) = S_{y}(f(h(y))$ for…

In this note we describe the dual and the completion of the space of finite linear combinations of $(p,\infty)$-atoms, $0<p\leq 1$ on ${\mathbb R}^n$. As an application, we show an extension result for operators uniformly bounded on…

Let $A_p(G)$ denote the Figa-Talamanca-Herz Banach Algebra of the locally compact group}} $G$, thus $A_2(G)$ {\it{is the Fourier Algebra of $G$. If $G$ is commutative then $A_2(G)=L^1(\hat{G})^\wedge$. Let $A_p^r(G)=A_p\cap L^r(G)$ with…

Let $0<p<\infty$, $\Gamma$ 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 analytic functions $F$ satisfying…

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…

Let $(X, d, \mu)$ be a space of homogeneous type, i.e. the measure $\mu$ satisfies doubling (volume) property with respect to the balls defined by the metric $d$. Let $L$ be a non-negative self-adjoint operator on $L^2(X)$. Assume that the…

We study random unconditionality of Dirichlet series in vector-valued Hardy spaces $\mathcal H_p(X)$. It is shown that a Banach space $X$ has type 2 (respectively, cotype 2) if and only if for every choice $(x_n)_n\subset X$ it follows that…

Let $(X, Y)$ be a couple of quasi-Banach lattices of measurable functions on $\mathbb T \times \Omega$ satisfying some additional assumptions. The K-closedness of a couple of Hardy-type spaces $(X_A, Y_A)$ in $(X, Y)$ and the stability of…

In this paper we study Hardy spaces associated with non-negative self-adjoint operators and develop their vector-valued theory. The complex interpolation scales of vector-valued tent spaces and Hardy spaces are extended to the endpoint p=1.…

A Haar system Hardy space is the completion of the linear span of the Haar system $(h_I)_I$, either under a rearrangement-invariant norm $\|\cdot \|$ or under the associated square function norm \begin{equation*} \Bigl\| \sum_Ia_Ih_I…

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…

We study Hausdorff-Young type inequalities for vector-valued Dirichlet series which allow to compare the norm of a Dirichlet series in the Hardy space $\mathcal{H}_{p} (X)$ with the $q$-norm of its coefficients. In order to obtain…

A well-known result going back to the 1930s states that all bounded linear operators mapping scalar-valued $L^1$-spaces into $L^\infty$-spaces are kernel operators and that in fact this relation induces an isometric isomorphism between the…

We present a generalization of H\"older duality to algebra-valued pairings via $L^p$-modules. H\"older duality states that if $p \in (1, \infty)$ and $p^{\prime}$ are conjugate exponents, then the dual space of $L^p(\mu)$ is isometrically…

Let $(X,\mu)$ be a space with a finite measure $\mu$, let $A$ and $B$ be $w^*$-closed subalgebras of $L^{\infty}(\mu)$, and let $C$ and $D$ be closed subspaces of $L^p(\mu)$ ($1<p<\infty$) that are modules over $A$ and $B$, respectively.…

Let ${\mathcal X}$ be a space of homogeneous type in the sense of Coifman and Weiss and ${\mathcal D}$ a collection of balls in $\cx$. The authors introduce the localized atomic Hardy space $H^{p, q}_{\mathcal D}({\mathcal X})$ with $p\in…

In this paper, we introduce the notion of martingale Hardy-amalgam spaces: $ H^s_{p,q},\,\,\mathcal{Q}_{p,q}$ and $\mathcal{P}_{p,q}$. We present two atomic decompositions for these spaces. The dual space of $H^s_{p,q}$ for $0<p\le q\le 1$…