Sobolev subspaces of nowhere bounded functions
Functional Analysis
2023-09-07 v1
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 functions for suitable values of larger than the Sobolev exponent.
Keywords
Cite
@article{arxiv.1605.00233,
title = {Sobolev subspaces of nowhere bounded functions},
author = {Pier Domenico Lamberti and Giorgio Stefani},
journal= {arXiv preprint arXiv:1605.00233},
year = {2023}
}
Comments
To appear in the journal Real Analysis Exchange http://msupress.org/journals/raex/