One-way functions with respect to various resource bounds
Regarding log-space:  Several candidate one-way functions are computable in log-space or below (and are supposedly secure even against poly-time adversaries).  You can find several pointers for example in the Cryptography in NC$^0$ paper.

Two specific examples include:

Integer multiplication (there are some subtleties for standard OWF, but if you only care about worst-case this is enough)

The Impagliazzo-Naor candidate based on subset-sum:
$f(a_1,...,a_n,S) := (a_1,..., a_n, \sum_{i \in S} a_i \mod 2^n)$.