Vol. 3 No. 1 (2010)

In this paper we consider an example on asymptotic expansions on manifolds with corner singularities. The content is a helpful step to understand how affects the push--forward operation under a $b$-fibration on the asymptotic data on basic objects, namely on $b$-densities.

If $\mathscr{F}$ is a non-empty Fitting class, $\pi=\pi(\mathscr{F})$ and $G$ a group such that every chief factor of $G/G_{\mathscr{F}}$ is an $C_{\pi}^{s}$-group. Then $G$ has at least one $\mathscr{F}$-injector. This result is used to resolve an open problem and generalize some known results.

In this note we call attention to the fact that there exist some relations between the Matuszewska-Orlicz indices $m(\varphi)$ and $M(\varphi)$ of the function $\varphi$, and possible values of the constants in Zygmund type inequalities.