Related papers: Multi-normed spaces, based on non-discrete measure…

Let $n_j$ be a lacunary sequence of integers, such that $n_{j+1}/n_j\geq r$. We are interested in linear combinations of the sequence of finite Riesz products $\prod_{j=1}^N(1+\cos(n_j t))$. We prove that, whenever the Riesz products are…

We prove that for $1\le p,q\le\infty$ the mixed-norm spaces $L_q(L_p)$ are mutually non-isomorphic, with the only exception that $L_q(L_2)$ is isomorphic to $L_q(L_q)$ for all $1<q<\infty$.

A well-known result by Lindenstrauss is that any two-dimensional normed space can be isometrically imbedded into $L_1(0,1)$. We provide an explicit form of a such an imbedding. The proof is elementary and self-contained. Applications are…

We define 2-indexed $(q,p)$-Schatten quasi-norms for any $q,p > 0$ on operators on a tensor product of Hilbert spaces, naturally extending the norms defined by Pisier's theory of operator-valued Schatten spaces. We establish several…

Enflo and Rosenthal proved that $\ell_p(\aleph_1)$, $1 < p < 2$, does not (isomorphically) embed into $L_p(\mu)$ with $\mu$ a finite measure. We prove that if $X$ is a subspace of an $L_p$ space, $1< p < 2$, and $\ell_p(\aleph_1)$ does not…

In the last decade, the problem of characterizing the normability of the weighted Lorentz spaces has been completely solved (\cite{Sa}, \cite{CaSoA}). However, the question for multidimensional Lorentz spaces is still open. In this paper,…

Let $p\in(0, 1]$. In this paper, the authors prove that a sublinear operator $T$ (which is originally defined on smooth functions with compact support) can be extended as a bounded sublinear operator from product Hardy spaces $H^p({{\mathbb…

A uniform strategy to derive metric tensors in two spatial dimension for interpolation errors and their gradients in $L^p$ norm is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in corresponding metric space, with…

Given a strictly increasing sequence $\Lambda=(\lambda_n)$ of nonegative real numbers, with $\sum_{n=1}^\infty \frac{1}{\lambda_n}<\infty$, the M\"untz spaces $M_\Lambda^p$ are defined as the closure in $L^p([0,1])$ of the monomials…

We use the theory of quantization to introduce non-commutative versions of metric on state space and Lipschitz seminorm. We show that a lower semicontinuous matrix Lipschitz seminorm is determined by their matrix metrics on the matrix state…

For a general measure space $(\Omega,\mu)$, it is shown that for every band $M$ in $L_p(\mu)$ there exists a decomposition $\mu=\mu'+\mu^{\prime\prime}$ such that $M=L_p(\mu')=\{f\in L_p(\mu);f=0\ \mu^{\prime\prime}\text{-a.e.}\}$. The…

Given a positive integer $n$ and a partition $(n_1,\ldots,n_r)$ of $n$, one can consider the associated $n$-dimensional multiprojective space $\mathbb{P}^{n_1}\times \cdots \times \mathbb{P}^{n_r}$. These multiprojective spaces are…

Let $\mathcal{L}$ be a first-order two-sorted language. Let $S$ be some fixed structure. A standard structure is an $\mathcal{L}$-structure of the form $(M,S)$, where $M$ is arbitrary. When $S$ is a compact topological space (and…

We estimate the $L^{p}$ norms of the discrepancy between the volume and the number of integer points in $r\Omega-x$, a dilated by a factor $r$ and translated by a vector $x$ of a convex body $\Omega$ in $\mathbb{R}^{d}$ with smooth boundary…

Based on a suitable improvement of a triangle inequality, we derive new mutual bounds for $p$-angular distance $\alpha_p[x,y]=\big\Vert \Vert x\Vert^{p-1}x- \Vert y\Vert^{p-1}y\big\Vert$, in a normed linear space $X$. We show that our…

We consider 1-complemented subspaces (ranges of contractive projections) of vector-valued spaces $\ell_p(X)$, where $X$ is a Banach space with a 1-unconditional basis and $p \in (1,2)\cup (2,\infty)$. If the norm of $X$ is twice…

Three themes of general topology: quotient spaces; absolute retracts; and inverse limits - are reapproached here in the setting of metrizable uniform spaces, with an eye to applications in geometric and algebraic topology. The results…

The Littlewood-Richardson coefficients describe the decomposition of tensor products of irreducible representations of a simple Lie algebra into irreducibles. Assuming the number of factors is large, one gets a measure on the space of…

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…

We consider the mixed norm spaces of Hardy type studied by Flett and others. We study some properties of these spaces related to mean and pointwise growth and complement some partial results by various authors by giving a complete…