Lineability of non-differentiable Pettis primitives

关于无处可微函数的(n,ℵ₀)-线性无关性

On the $(n,\aleph_0)$-Lineability of Nowhere Differentiable Functions

研究连续无处可微函数族的可数维扩展性质，通过证明可将特定有限维子空间扩展为可数无限维子空间，为相关函数族性质研究提供新成果。

Factorization Theorem through a Dunford-Pettis $p$-convergent operator

In this article, we introduce the notion of $p$-$(DPL)$ sets.\ Also, a factorization result for differentiable mappings through Dunford-Pettis $p$-convergent operators is investigated.\ Namely, if $ X ,Y $ are real Banach spaces and $U$ is an open convex subset of $X,$ then we obtain that, given a differentiable mapping $f: U\rightarrow Y$ its derivative $f^{\prime}$ takes $U$-bounded sets into $p$-$(DPL)$ sets if and only if it happens $f=g\circ S,$ where $S$ is a Dunford-Pettis $p$-convergent operator from $X$ into a suitable Banach space $Z$ and $g:S(U)\rightarrow Y$ is a Gâteaux differenti…

无限逐点线性性：一般准则与应用

Infinite pointwise lineability: general criteria and applications

本文提出无限逐点稠密线性性概念，给出从线性性到稠密性的准则，并应用于研究无界可微可积函数的线性与拓扑结构。

Lineability in sequence and function spaces

It is proved the existence of large algebraic structures \break --including large vector subspaces or infinitely generated free algebras-- inside, among others, the family of Lebesgue measurable functions that are surjective in a strong sense, the family of nonconstant differentiable real functions vanishing on dense sets, and the family of non-continuous separately continuous real functions. Lineability in special spaces of sequences is also investigated. Some of our findings complete or extend a number of results by several authors.

Nowhere Weak Differentiability of the Pettis Integral

For an arbitrary infinite-dimensional Banach space $\X$, we construct examples of strongly-measurable $\X$-valued Pettis integrable functions whose indefinite Pettis integrals are nowhere weakly differentiable; thus, for these functions the Lebesgue Differentiation Theorem fails rather spectacularly. We also relate the degree of nondifferentiability of the indefinite Pettis integral to the cotype of $\X$, from which it follows that our examples are reasonably sharp. This is an expanded version of a previously posted paper with the same name.

Some properties of differentiable p-adic functions

In this paper, using the tools from the lineability theory, we distinguish certain subsets of $p$-adic differentiable functions. Specifically, we show that the following sets of functions are large enough to contain an infinite dimensional algebraic structure: (i) continuously differentiable but not strictly differentiable functions, (ii) strictly differentiable functions of order $r$ but not strictly differentiable of order $r+1$, (iii) strictly differentiable functions with zero derivative that are not Lipschitzian of any order $α>1$, (iv) differentiable functions with unbounded derivative, …