Published Paper

Inserted: 3 oct 2021

Journal: Real Anal. Exchange
Volume: 41
Number: 2
Pages: 367--375
Year: 2016

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.

Keywords: Sobolev spaces, Nowhere bounded functions, Sobolev Embedding