Related papers: Complex interpolation of Hardy-type subspaces

We studied complex interpolation noncommutative Hardy space associated with semi-finite von Neumann algebra and extend Pisier's interpolation theorem for this case.

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.…

Given a sequence of points in the unit disk, a well known result due to Carleson states that if given any point of the sequence it is possible to interpolate the value one in that point and zero in all the other points of the sequence, with…

We introduce connections between the Cuntz relations and the Hardy space H_2 of the open unit disk . We then use them to solve a new kind of multipoint interpolation problem in H_2, where for instance, only a linear combination of the…

Given an inner function $\theta$ on the unit disk, let $K^p_\theta:=H^p\cap\theta\bar z\bar{H^p}$ be the associated star-invariant subspace of the Hardy space $H^p$. Also, we put $K_{*\theta}:=K^2_\theta\cap{\rm BMO}$. Assuming 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…

Given $E_0, E_1, F_0, F_1, E$ rearrangement invariant function spaces, $a_0$, $a_1$, $b_0$, $b_1$, $b$ slowly varying functions and $0< \theta_0<\theta_1<1$, we characterize the interpolation spaces $$(\overline{X}^{\mathcal…

Given an inner function $\theta$, the associated star-invariant subspace $K^\infty_\theta$ is formed by the functions $f\in H^\infty$ that annihilate (with respect to the usual pairing) the shift-invariant subspace $\theta H^1$ of the Hardy…

We consider $K$-interpolation spaces involving slowly varying functions, and derive necessary and sufficient conditions for a Holmstedt-type formula to be held in the limiting case $\theta_0=\theta_1\in\{0,1\}.$ We also study the case…

In this paper, we present the complex interpolation of Besov and Triebel-Lizorkin spaces with generalized smoothness. In some particular cases these function spaces are just weighted Besov and Triebel-Lizorkin spaces. An application, we…

Let $(X, Y)$ be a suitable couple of quasi-Banach lattices of measurable functions on $\mathbb T \times \Omega$, and let $(X_A, Y_A)$ be the couple of the corresponding Hardy-type spaces. It has long been suspected that the BMO-regularity…

In the paper Description of the $K$-spaces by means of $J$-spaces and the reverse problem, Math. Nachr. 296 (2023), no. 9, 4002--4031, we have establish conditions under which the limiting $K$-space $(X_0,X_1)_{0,q,b;K}$, involving a slowly…

We prove that atomic decomposition for the Hardy spaces h_1 and H_1 is valid for noncommutative martingales. We also establish that the conditioned Hardy spaces of noncommutative martingales h_p and bmo form interpolation scales with…

Given an interpolating Blaschke product $B$ with zeros $\{a_j\}$, we seek to characterize the sequences of values $\{w_j\}$ for which the interpolation problem $$f(a_j)=w_j\qquad (j=1,2,\dots)$$ can be solved with a function $f$ from the…

Given a finite set $\sigma$ of the unit disc $\mathbb{D}$ and a holomorphic function $f$ in $\mathbb{D}$ which belongs to a class $X$ we are looking for a function $g$ in another class $Y$ which minimizes the norm $|g|_{Y}$ among all…

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.…

Our starting point is a lemma due to Varopoulos. We give a different proof of a generalized form this lemma, that yields an equivalent description of the $K$-functional for the interpolation couple $(X_0,X_1)$ where…

This paper can be considered as the sequel of [6], where the authors have proposed an abstract construction of Hardy spaces H^1. They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more…

The real and complex interpolation spaces for the classical Hardy spaces $H^1$ and $H^\infty$ were determined in 1983 by P.W. Jones. Due to the analytic constraints the associated Marcinkiewicz decomposition gives rise to a delicate…

M. Daher [9] showed that if $(X_0, X_1)$ is a regular couple of uniformly convex spaces then the unit spheres of the complex interpolation spaces $X_{\theta}$ and $X_{\eta}$ are uniformly homeomorphic for every $0 < \theta, \eta < 1$. We…