He was a member of several scientific societies. From 1930 until 1952 he was a member of the [[Warsaw Scientific Society]] (''TNW''), from 1946 a member of the [[Polish Academy of Learning]] (''PAU''), from 1959 a member of the [[Polish Academy of Sciences]] (''PAN''), and from 1961 a member of the [[National Academy of Science]] in [[Washington, D.C.]]. In 1986 he received the [[National Medal of Science]].
His main interest was [[harmonic analysis]]. He wrote in Polish what soon became, in its English translation, the standard text in analysis, the two-volume ''[[Trigonometric Series]]''. His students included [[Alberto Calderón]], [[Paul Cohen (mathematician)|Paul Cohen]], [[Nathan Fine]], [[Józef Marcinkiewicz]], [[Victor L. Shapiro]], [[Guido Weiss]], [[Elias M. Stein|Elias Stein]] and Misha Cotlar. He died in [[Chicago]].
His work has had a pervasive influence in many fields of mathematics, particularly in [[mathematical analysis]]. Perhaps most important was his work with Calderón on [[singular integral operator]]s.