English

On the pointwise domination of a function by its maximal function

Classical Analysis and ODEs 2018-12-06 v2

Abstract

We show that under rather general circumstances, the almost everywhere pointwise inequality f(x)Mf(x)|f|(x) \le Mf (x) is equivalent to a weak form of the Lebesgue density theorem, for totally bounded closed sets. We derive both positive and negative results from this characterization.

Keywords

Cite

@article{arxiv.1710.02033,
  title  = {On the pointwise domination of a function by its maximal function},
  author = {J. M. Aldaz},
  journal= {arXiv preprint arXiv:1710.02033},
  year   = {2018}
}

Comments

13 pages, incorporates suggestions by a referee

R2 v1 2026-06-22T22:04:42.835Z