Related papers: Interpolating sequences for some subsets of analyt…

We develop a comprehensive theory for a general class of multi-parameter function spaces of Besov-Triebel-Lizorkin type, with a matrix weight. We prove the equivalence of different quasi-norms, the identification of function and sequence…

We investigate the problem of establishing bilateral continuous embeddings of the uniformly localized Bessel potential spaces $H^{\gamma}_{r, \: unif}(\mathbb{R}^n)$ into the multiplier spaces between Bessel potential spaces with positive…

The classic example of a low-discrepancy sequence in $\mathbb{Z}_p$ is $(x_n) = an+b$ with $a \in \mathbb{Z}_p^x$ and $b \in \mathbb{Z}_p$. Here we address the non-linear case and show that a polynomial $f$ generates a low-discrepancy…

In this paper, the author establishes some interpolation results between Lorentz, Morrey and BMO spaces. Let $1<p<\infty$ and $p\leq r\leq\infty$. It is proved that the space $L^{p,r}(\mathbb R^n)\cap\mathrm{BMO}(\mathbb R^n)$ is…

Let $0<p<q\leq\infty$ and $\alpha \in (0,\infty]$. We give a characterization of quasi-Banach interpolation spaces for the couple $(L_p(0,\alpha),L_q(0,\alpha))$ in terms of two monotonicity properties, extending known results which mainly…

This paper initiates the study of the structure of a new class of $p$-Banach spaces, $0<p<1$, namely the Lipschitz free $p$-spaces (alternatively called Arens-Eells $p$-spaces) $\mathcal{F}_{p}(\mathcal{M})$ over $p$-metric spaces. We…

Let N and M be von Neumann algebras. It is proved that L^p(N) does not Banach embed in L^p(M) for N infinite, M finite, 1 < or = p < 2. The following considerably stronger result is obtained (which implies this, since the Schatten p-class…

We present a constructive method to compute the cellularization with respect to K(Z/p, m) for any integer m > 0 of a large class of H-spaces, namely all those which have a finite number of non-trivial K(Z/p, m)-homotopy groups (the pointed…

Let $\mathcal{M}$ be a semifinite von Nemann algebra equipped with an increasing filtration $(\mathcal{M}_n)_{n\geq 1}$ of (semifinite) von Neumann subalgebras of $\M$. For $0<p \leq\infty$, let $\h_p^c(\mathcal{M})$ denote the…

We extend our work on nonseparated interpolating sequences, originally developed for Bergman spaces with weights of the form $(1 - |z|^2)^\alpha$, to more general weights.

A Banach lattice E is called p-disjointly homogeneous, 1< p< infty, when every sequence of pairwise disjoint normalized elements in E has a subsequence equivalent to the unit vector basis of l_p. Employing methods from interpolation theory,…

This paper investigates cross correlation properties of sequences derived from GH sequences modulo p, where p is a prime number and presents comparison with cross correlation properties of pseudo noise sequences. For GH sequences modulo…

This paper is concerned with proving some embeddings of the form \begin{equation*} F_{p_{1},q}^{s_{1}}\cdot B_{p_{2},\infty }^{s_{2}}\cdot ...\cdot B_{p_{m},\infty }^{s_{m}}\hookrightarrow F_{p,q}^{s_{1}},\quad m\geq 2. \end{equation*} The…

Continuing previous work, this paper provides maximal characterizations of anisotropic Triebel-Lizorkin spaces $\dot{\mathbf{F}}^{\alpha}_{p,q}$ for the endpoint case of $p = \infty$ and the full scale of parameters $\alpha \in \mathbb{R}$…

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…

Let 1\leq p<2 and let L_p=L_p[0,1] be the classical L_p-space of all (classes of) p-integrable functions on [0,1]. It is known that a sequence of independent copies of a mean zero random variable f from L_p spans in L_p a subspace…

We compare the Kolmogorov and entropy numbers of compact operators mapping from a Hilbert space into a Banach space. We then apply these general findings to embeddings between reproducing kernel Hilbert spaces and $L_\infty(\mu)$. Here we…

For $p > 1, \gamma \in \mathbb{R}$, denote by $H^{\gamma}_p(\mathbb{R}^n)$ the Bessel potential space, by $H^{\gamma}_{p, unif}(\mathbb{R}^n)$ the corresponding uniformly localized Bessel potential space and by $M[s, -t]$ the space of…

Let $\mathcal{M}$ be a $\sigma$-finite von Neumann algebra, equipped with a normal faithful state $\varphi$, and let $\mathcal{A}$ be a maximal subdiagonal subalgebra of $\mathcal{M}$. We have proved that for $0< p<1$, $H^p(\mathcal{A})$ is…

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…