Related papers: Weak factorization of Hardy spaces in the Bessel s…

We explore commutativity up to a factor, $AB=\lambda BA$, for bounded operators in a complex Hilbert space. Conditions on the possible values of the factor $\lambda$ are formulated and shown to depend on spectral properties of the operators…

For a given weighted mean $\mathscr{M}$ defined on a subinterval of $\mathbb{R}_+$ and a sequence of weights $\lambda=(\lambda_n)_{n=1}^\infty$ we define a Hardy constant $\mathscr H(\lambda)$ as the smallest extended real number such that…

In this paper, we further investigate the problem of commutativity up to a factor (or $\lambda$-commutativity) in the setting of bounded and unbounded linear operators in a complex Hilbert space. The results are based on a new approach to…

We derive a family of weighted Hardy-type inequalities in the variable exponent Lebesgue space with an additional term of the form \[ \int_\Omega\ |\xi|^{p(x)} \mu_{1,\beta}(dx)\leqslant \int_\Omega |\nabla…

Let $T$ be a linear operator that, for some $p_1\in(1,\infty)$, is bounded on $L^{p_1}(\tilde w)$ for all $\tilde w\in A_{p_1}(\mathbb R^d)$ and in addition compact on $L^{p_1}(w_1)$ for some $w_1\in A_{p_1}(\mathbb R^d)$. Then $T$ is…

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…

We establish the boundedness of the multilinear Calder\'on-Zygmund operators from a product of weighted Hardy spaces into a weighted Hardy or Lebesgue space. Our results generalize to the weighted setting results obtained by Grafakos and…

For any Calder\'on-Zygmund operator $ T$, any weight $ w$, and $ \alpha >1$, the operator $ T$ is bounded as a map from $ L ^{1} (M _{ L \log\log L (\log\log\log L) ^{\alpha } } w )$ into weak-$L^1(w)$. The interest in questions of this…

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…

The boundedness and compactness of weighted composition operators on the Hardy space ${\mathcal H}^2$ of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schatten-class…

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…

Let $\Gamma$ be a graph with the doubling property for the volume of balls and $P$ a reversible random walk on $\Gamma$. We introduce $H^1$ Hardy spaces of functions and $1$-forms adapted to $P$ and prove various characterizations of these…

Let $M$ be the Hardy-Littlewood maximal function. Denote by $M_b$ and $[b,M]$ the maximal and the nonlinear commutators of $M$ with a function $b$. The boundedness of $M_b$ and $[b,M]$ on weighted Lebesgue spaces are characterized when the…

We estudy the $H^{p}(\mathbb{Z})$ - $\ell^{q}(\mathbb{Z})$ boundedness of the fractional series operator $T_{\gamma}$ given by \[ (T_{\gamma}b)(j) = \sum_{i \neq \pm j} \frac{b(i)}{|i-j|^{\alpha}|i+j|^{\beta}}, \] where $0 \leq \gamma < 1$,…

It is shown how any contractive multiplier from the Hardy space to a weighted Hardy space $H^{2}_{\bbeta}$ can be factored as a fixed factor composed with the classical Schur multiplier (contractive multiplier between Hardy spaces). The…

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…

We introduce Hardy spaces for martingales with respect to continuous filtration for von Neumann algebras. In particular we prove the analogues of the Burkholder/Gundy and Burkholder/Rosenthal inequalities in this setting. The usual…

In this paper, we first study the sharp weak estimate for the $p$-adic $n$-dimensional fractional Hardy operator from $L^p$ to $L^{q,\infty}$. Secondly, we study the sharp bounds for the $m$-linear $n$-dimensional $p$-adic integral operator…

The well known result of Bourgain and Kwapie\'n states that the projection $P_{\leq m}$ onto the subspace of the Hilbert space $L^2\left(\Omega^\infty\right)$ spanned by functions dependent on at most $m$ variables is bounded in $L^p$ with…

Let $\mathcal H$ be the Drury-Arveson or Dirichlet space of the unit ball of $\mathbb C^d$. The weak product $\mathcal H\odot\mathcal H$ of $\mathcal H$ is the collection of all functions $h$ that can be written as $h=\sum_{n=1}^\infty f_n…