English

The Law of the iterated logaritm for smooth functions

Classical Analysis and ODEs 2026-05-20 v1

Abstract

A version of the Law of the Iterated Logarithm for smooth functions in the upper-half space is proved. As a consequence, we show that certain size conditions on the gradient and the gradient of the laplacian of a smooth function, lead to self-improvement growth properties. The results are applied in situations where harmonicity is not present.

Keywords

Cite

@article{arxiv.2605.20018,
  title  = {The Law of the iterated logaritm for smooth functions},
  author = {José G. Llorente and Artur Nicolau},
  journal= {arXiv preprint arXiv:2605.20018},
  year   = {2026}
}

Comments

18 pages