We present the full descriptive characterizations of the strong McShane integral (or the variational McShane integral) of a Banach space valued function $f:W\to X$ defined on a non-degenerate closed subinterval $W$ of ${ℝ}^m$ in terms of strong absolute continuity or, equivalently, in terms of McShane variational measure $V_{ℳ}F$ generated by the primitive $F:{ℐ}_W\to X$ of $f$, where ${ℐ}_W$ is the family of all closed non-degenerate subintervals of $W$.

We study the relation between standard ideals of the convolution Sobolev algebra ${₊}^{\left(n\right)}\left(tⁿ\right)$ and the convolution Beurling algebra L¹((1+t)ⁿ) on the half-line (0,∞). In particular it is proved that all closed ideals in ${₊}^{\left(n\right)}\left(tⁿ\right)$ with compact and countable hull are standard.