I am reading Hildebrandt's and Widman's 1975 paper on "Some regularity results of quasilinear elliptic systems of second order".

Theorem 3.1 is the first time in their paper that the function space $H^1_{m, \sigma}(\Omega',\mathbb{R}^N)$ for $\sigma\in (0, 1)$ appears.

Any idea what this space is? I know that $H^1_m$ is the Sobolev space $W^{1, m}$, but what does it mean when there is a $\sigma\in (0, 1)$?