He was a member of several scientific societies. From 1930 until 1952 he was a member of the Polish [[Society of Friends of Science]] (''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 a standard two-volume work ''[[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]].
His work has had a pervasive influence in many fields of mathematics, particularly in [[mathematical analysis]]. He wrote over 6 books.{{Citation needed|date=July 2011}} Perhaps most important was his work with Calderón on [[singular integral operator]]s.
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