The multiresolution expansion $\{E_jf\}_{j\in\mathbb N}$, $f\in\mathcal D'_{L^q}(\mathbb R^n)$, $1\leq q\leq\infty$, is defined via a scaling function which order of regularity is equal to the order of $f$. Abelian and Tauberian type theorems for the quasiasymptotic behavior at infinity of distributions from $\mathcal D'L^q(\mathbb R^n)$ related to the quasiasymptotic behavior at infinity of its projections $E_jf$, $j\in\mathbb N$, are given.