English

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 LqL^q functions for suitable values of qq 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/

R2 v1 2026-06-22T13:45:42.502Z