Differential forms on log canonical spaces in positive characteristic

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