Related papers: Embeddings between sequence variable Lebesgue spac…

In this paper, we investigate linear systems on hyperelliptic varieties. We prove analogues of well-known theorems on abelian varieties, like Lefschetz's embedding theorem and higher k-jet embedding theorems. Syzygy or $N_p$-properties are…

The first part of this paper surveys several results on the lattice structure of variable exponent Lebesgue function spaces (or Nakano spaces) $\lpv$. In the second part strictly singular and disjointly strictly singular operators between…

It is shown in this note that one can decide whether an $n$-dimensional subspace of $\ell_\infty^N$ is isometrically isomorphic to $\ell_\infty^n$ by testing a finite number of determinental inequalities. As a byproduct, an elementary proof…

We describe certain sufficient conditions for an infinitely divisible probability measure on a class of connected Lie groups to be embeddable in a continuous one-parameter convolution semigroup of probability measures. (Theorem 1.3). This…

We say that a finite metric space $X$ can be embedded almost isometrically into a class of metric spaces $C$, if for every $\epsilon > 0$ there exists an embedding of $X$ into one of the elements of $C$ with the bi-Lipschitz distortion less…

A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper…

We investigate the properties of the variable Lebesgue spaces with quasi-norm on a probability space, and give the atomic decompositions suited to the variable exponent martingale Hardy spaces. Using the decompositions and the harmonic mean…

New partial results are obtained related to the following old problem of Erd\"os: for any infinite set $X$ of real numbers to show that there is always a measurable (or, equivalently, closed) subset of reals of positive Lebesgue measure…

In this paper, we generalize a recently obtained result by Kopaliani and Zviadadze from the one-variable case to the several-variable case. Specifically, in terms of decreasing rearrangement, we characterize those exponents $p(\cdot)$ for…

We establish conditions on the parameters which are both necessary and sufficient in order that Besov and Triebel-Lizorkin spaces of generalized smoothness contain only regular distributions. We also connect this with the possibility of…

We study the classical spaces $L_{p}$ and $\ell_{p}$ for the whole range $0<p<\infty$ from a metric viewpoint and give a complete Lipschitz embeddability roadmap between any two of those spaces when equipped with both their ad-hoc distances…

Suppose that the (normalised) partial sum of a stationary sequence converges to a standard normal random variable. Given sufficiently moments, when do we have a rate of convergence of $n^{-1/2}$ in the uniform metric, in other words, when…

In this paper we obtain order estimates for entropy numbers of embeddings of weighted Sobolev spaces into weighted Lebesgue spaces and of weighted summation operators on trees. Here we consider some critical conditions on the parameters.

We consider the question as to whether the exponent of a computably presentable Lebesgue space whose dimension is at least 2 must be computable. We show this very natural conjecture is true when the exponent is at least 2 or when the space…

We prove that any two algebraic embeddings of $\mathbb{C}$ into $\textrm{SL}_n(\mathbb{C})$ are the same up to an algebraic automorphism of $\textrm{SL}_n(\mathbb{C})$, provided that $n$ is at least $3$. Moreover, we prove that two…

We give necessary and sufficient conditions for the embeddings $\Lambda\text{BV}^{(p)}\subseteq \Gamma\text{BV}^{(q_n\uparrow q)}$ and $\Phi\text{BV}\subseteq\text{BV}^{(q_n\uparrow q)}$. As a consequence, a number of results in the…

We prove that the sequence space $\ell_{p,q}$ does not embed into $L_{p,q}(\mathcal{M},\tau)$ for any noncommutative probability space $(\mathcal{M},\tau)$, $1< p<\infty $, $1\le q<\infty$, $p\ne q$. Several applications to the isomorphic…

We study the existence of cubic quotients of finite-dimensional quasi-normed spaces, that is, quotients well isomorphic to $\ell_{\infty}^k$ for some $k.$ We give two results of this nature. The first guarantees a proportional dimensional…

We investigate the norm of sums of independent vector-valued random variables in noncommutative Lp spaces. This allows us to obtain a uniform family of complete embeddings of the Schatten class Sq^n in Sp(lq^m) with optimal order m = n^2.…

The paper is devoted to restricted Oppenheim expansion of real numbers ($ROE$),which includes as partial cases already known Engel, Silvester and L\"uroth expansions. We find conditions under which for almost all (with respect to Lebesgue…