Year: 2011
Type: preprint
Abstract: We say that a function $f:[0,1]\rightarrow \R$ is \emph{nowhere $L^q$} if, for each nonvoid open subset $U$ of $[0,1]$, the restriction $f|_U$ is not in $L^q(U)$. For a fixed $1 \leq p p} L_q[0,1]$ is spaceable for every $p>0$, preprint, 2011., since $S_p$ turns out to be spaceable. In addition, our result is a generalization of one of the main results from S. Głcab, P. L. Kaufmann, and L. Pellegrini, Spaceability and algebrability of sets of nowhere integrable functions, preprint, 2011.
Source: arXiv (Cornell University)
Authors: Kaufmann, Pedro L., Pellegrini, Leonardo
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2099525154