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.
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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}
}
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18 pages