This is an announcement for the paper "Spaceability of sets of nowhere $L^q$ functions" by Pedro L. Kaufmann and Leonardo Pellegrini.

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 $1\leq p <\infty$, we will show that the set $$ S_p\doteq {f\in L^p[0,1]: f\mbox{ is nowhere $L^q$, for each }p<q\leq\infty}, $$ united with ${0}$, contains an isometric and complemented copy of $\ell_p$. In particular, this improves a result from G. Botelho, V. F'avaro, D. Pellegrino, and J. B. Seoane-Sep'ulveda, $L_p[0,1]\setminus \cup_{q>p} L_q[0,1]$ 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. G\l \c ab, P. L. Kaufmann, and L. Pellegrini, Spaceability and algebrability of sets of nowhere integrable functions, preprint, 2011.

Archive classification: math.FA

Mathematics Subject Classification: 26A30

Submitted from: leoime@yahoo.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/abs/1110.5774

or

http://arXiv.org/abs/abs/1110.5774