Related papers: Interpolation of Ces{\`a}ro sequence and function …

We consider the problem of complex interpolation of certain Hardy-type subspaces of K\"othe function spaces. For example, suppose $X_0$ and $X_1$ are K\"othe function spaces on the unit circle $\bold T,$ and let $H_{X_0}$ and $H_{X_1}$ be…

The functional interpolation problem on a continual set of nodes by an integral continued C-fraction is studied. The necessary and sufficient conditions for its solvability are found. As a particular case, the considered integral continued…

We give the characterization of the embeddings between weighted Tandori and Ces\`{a}ro function spaces using the combination of duality arguments for weighted Lebesgue spaces and weighted Tandori spaces with estimates for the iterated…

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…

The spectrum of the Ces\`aro operator $\mathsf{C}$ is determined on the spaces which arises as intersections $A^p_{\alpha +}$ (resp. unions $A^p_{\alpha -}$) of Bergman spaces $A_\alpha^p$ of order $1<p<\infty$ induced by standard radial…

Generalized Ces\`aro operators $C_t$, for $t\in [0,1)$, are investigated when they act on the disc algebra $A(\mathbb{D})$ and on the Hardy spaces $H^p$, for $1\leq p \leq \infty$. We study the continuity, compactness, spectrum and point…

Interpolation inequalities in Triebel-Lizorkin-Lorentz spaces and Besov-Lorentz spaces are studied for both inhomogeneous and homogeneous cases. First we establish interpolation inequalities under quite general assumptions on the parameters…

We consider Ces\'aro operator on the Hardy space $H^p(\mathbb{C}_+)$ in the upper half-plane for $1<p<\infty$. In \cite{AS} it was proved that for all $1<p<\infty$ the spectrum of the operator $V=\frac{2(p-1)}{p}C-I$ is located on the unit…

We consider a real interpolation method defined by means of slowly varying functions. We present some reiteration formulae including so called $L$ or $R$ limiting interpolation spaces. These spaces arise naturally in reiteration formulae…

The Rademacher series in rearrangement invariant function spaces "closed" to the space L_\infty are considered. In terms of interpolation theory of operators a correspondence between such spaces and spaces of coefficients generated by them…

We present the abstract framework and some applications of interpolation theory. The main new result concerns interpolation between H^1 and L^p estimates for analytic families of operators acting on Schwartz functions.

It is known (implicit in [HMNT]) that when $\Lambda$ is an interpolating sequence for the Nevanlinna or the Smirnov class then there exist functions $f_\lambda$ in these spaces, with uniform control of their growth and attaining values 1 on…

We prove that Ces\`{a}ro means of one-dimensional Walsh-Fourier series are uniformly bounded operators in the martingale Hardy space $H_{p}$ for $% 0<p<1/\left( 1+\alpha \right).$

Let $(A_0, A_1)$ be an interpolation couple, and let $B_j$ be the closure of $A_0^\ast \cap A_1^\ast$ in $A_j^\ast$, $j = 0, 1$. For every $\theta \in \, ]0, 1[$, there exists a natural one to one contraction $R^\theta : A^\theta…

We call $(a_1, \dots, a_n)$ an \emph{$r$-partial sequence} if exactly $r$ of its entries are positive integers and the rest are all zero. For ${\bf c} = (c_1, \dots, c_n)$ with $1 \leq c_1 \leq \dots \leq c_n$, let $S_{\bf c}^{(r)}$ be the…

We prove noncommutative Khintchine inequalities for all interpolation spaces between $L_p$ and $L_2$ with $p<2$. In particular, it follows that Khintchine inequalities hold in $L_{1,\infty}$. Using a similar method, we find a new…

A multiresolution analysis is a nested chain of related approximation spaces.This nesting in turn implies relationships among interpolation bases in the approximation spaces and their derived wavelet spaces. Using these relationships, a…

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…

We characterize Ces\`aro-Orlicz function spaces $Ces_\varphi$ containing isomorphic copy of $l^\infty$. We also describe the subspaces $(Ces_\varphi)_a$ of all order continuous elements of $Ces_\varphi$. Finally, we study the monotonicity…

In this article we study $p$-adic properties of sequences of integers (or $p$-adic integers) that satisfy a linear recurrence with constant coefficients. For such a sequence, we give an explicit approximate twisted interpolation to $\mathbb…