  Given a logarithmic $1$-form on the snc locus of a log canonical surface pair
$(X, D)$ over a perfect field of characteristic $p \ge 7$, we show that it
extends with at worst logarithmic poles to any resolution of singularities. We
also prove the analogous statement for regular differential forms, under an
additional tameness hypothesis. In addition, residue and restriction sequences
for tamely dlt pairs are established.
  We give a number of examples showing that our results are sharp in the
surface case, and that they fail in higher dimensions. On the other hand, our
techniques yield a new proof of the characteristic zero Logarithmic Extension
Theorem in any dimension.
