On the Bloch space and convolution of functions in the LpL^p-valued case

We introduce the convolution of functions in the vector valued spaces $H^1(L^P)$ and $H^1(L^q)$ by means of Young's Theorem, and we use this to show that Bloch functions taking values in certain space of operators define bilinear bounded maps in the product of those spaces for $1\leq p,q\leq 2$. As a corollary, we get a Marcinkiewicz-Zygmund type result

Classification of finite groups with many minimal normal subgroups and with the number of conjugacy classes of G/S(G)G/S(G) equal to 8

In this paper we classify all the finite groups satisfying $r(G/S(G))=8$ and $\beta(G)=r(G)-\alpha(G)-1$, where $r(G)$ is the number of conjugacy classes of $G,\beta(G)$ is the number of minimal normal subgroups of $G,S(G)$ the socle of $G$ and $\alpha(G)$ the number of conjugacy classes of $G$ out of $S(G)$. These results are a contribution to the general problem of the classification of the finite groups according to the number of conjugacy classes