Related papers: Some remarks on the interpolation space A^\beta

We prove a complex interpolation formula for the injective tensor product of vector-valued Banach function spaces satisfying certain geometric assumptions. This result unifies results of Kouba, and moreover, our approach offers an alternate…

We consider K-interpolation methods involving slowly varying functions. Let $\overline{A}_{\theta,*}^{\mathcal{L}}$ and $\overline{A}_{\theta,*}^{\mathcal{R}}$ $(0\leq\theta\leq1)$ be the so called ${\mathcal{L}}$ or ${\mathcal{R}}$…

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…

Kalton and Mitrea characterized complex interpolation spaces of quasi-Banach function spaces as Calder\'on products if both interpolants are separable. We show that one separability assumption may be omitted and establish a…

We study strict inclusion relations between approximation and interpolation spaces.

We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.

We formalize a technique for embedding Riemann sufraces properly into \C^2, and we generalize all known embedding results to allow interpolation on prescribed discrete sequences.

We solve an interpolation problem for computing $\zeta(2n)$ in a rather elementary way, by generalizing the main idea in \cite{SE}.

We study real and complex interpolation of abstract Ces\`aro, Copson and Tandori spaces, including the description of Calder\'on-Lozanovski{\v \i} construction for those spaces. The results may be regarded as generalizations of…

In this paper, we show that the interpolation spaces between Grand, small or classical Lebesgue are so called Lorentz-Zygmund spaces or more generally $G\Gamma$-spaces. As a direct consequence of our results any Lorentz-Zygmund space…

This paper extends the known characterization of interpolation and sampling sequences for Bergman spaces to the mixed-norm spaces. The Bergman spaces have conformal invariance properties not shared by the mixed-norm spaces. As a result,…

We treat interpolation for various logics.

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…

Let $E, F, E_0, E_1$ be rearrangement invariant spaces; let $a, \mathrm{b}, \mathrm{b}_0, \mathrm{b}_1$ be slowly varying functions and $0< \theta_0,\theta_1<1$. We characterize the interpolation spaces $$\Big(\overline{X}^{\mathcal…

We present a simple method based on the stability and duality of the properties of sampling and interpolation, which allows one to substantially simplify the proofs of some classical results.

Given $E_0, E_1, E, F$ rearrangement invariant spaces, $a, b, b_0, b_1$ slowly varying functions and $0\leq \theta_0<\theta_1\leq 1$, we characterize the interpolation space $$(\overline{X}_{\theta_0,b_0,E_0}, \overline{X}^{\mathcal…

In this paper, we introduce some difference sequence spaces in bigeometric calculus. We determine the $\alpha$-duals of these sequence spaces and study their matrix transformations. We also develop an interpolating polynomial in bigeometric…

In this paper we study two separate problems on interpolation. We first give some new equivalences of Stout's Theorem on necessary and sufficient conditions for a sequence of points to be an interpolating sequence on a finite open Riemann…

We study complex interpolation of weighted Besov and Lizorkin-Triebel spaces. The used weights $w_0,w_1$ are local Muckenhoupt weights in the sense of Rychkov. As a first step we calculate the Calder\'on products of associated sequence…

In this paper, we prove that the inner complex interpolation of two quasi-Banach lattices coincides with the closure of their intersection in their Calder\'on product. This generalizes a classical result by Shestakov in 1974 for Banach…