The study of Sobolev function spaces, which he introduced in the 1930s, immediately became a whole area of functional analysis . Sobolev's notion of generalised function (distribution) turned out to be especially important; with further developments by Schwartz and Gelfand, it became one of the central notions of mathematics.
Ang pag-aaral ng Sobolev function espasyo, kung saan siya ipinakilala sa 1930s, agad-agad na naging isang buong lugar ng functional analysis.