Distributions (as defined here) extend the definition of functions.
They were introduced to me as a linear form on locally integrable functions, and one could say that they're interesting because that linear form includes functions (i.e. to any $L^1_{loc}$ function we can associate a distribution), but the reverse isn't true (there isn't a bijection), so that we indeed can say that we've created a generalization of functions.
Therefore I was wondering, is there a linear form on distributions that is the equivalent of what distributions are to functions ? A kind of "distributions on distributions" ? If so, do they hold any mathematical interest ?