Sobolev subspaces of nowhere bounded functions

created by stefani on 03 Oct 2021

[BibTeX]

Published Paper

Inserted: 3 oct 2021

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

ArXiv: 1605.00233 PDF

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.

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