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He was a member of several scientific societies. From 1930 until 1952 he was a member of the Polish [[Society of Friends of Science]]{{disambiguation needed|date=November 2013}} (''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]], and [[Elias M. Stein|Elias Stein]]. He died in [[Chicago]]. He also liked chocolate ice cream.
 
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.