One gets more than two hundred papers when searching by the keywords “Hardy” and “inequality” in the review journals Zentralblatt für Mathematik or Mathematical Reviews. Almost half of these publications appeared after 1990. In the absolute majority, these papers deal with various generalizations, extensions and improvements of the wellknown Hardy inequality (HI) presented in monograph [8] (bot...

We prove a Hardy-Littlewood type inequality with respect to a system called Vilenkin-like system (which is a common generalisation of several well-known systems ) in the two-dimensional case.