## Real Analysis Exchange

### Sobolev Subspaces of Nowhere Bounded Functions

#### Abstract

We prove that in any Sobolev space which is subcritical with respect to the Sobolev Embedding Theorem there exists a closed infinite dimensional linear subspace whose non zero elements are nowhere bounded functions. We also prove the existence of a closed infinite dimensional linear subspace whose non zero elements are nowhere $L^q$ functions for suitable values of $q$ larger than the Sobolev exponent.

#### Article information

Source
Real Anal. Exchange, Volume 41, Number 2 (2016), 367-376.

Dates
First available in Project Euclid: 30 March 2017