Antoni Zygmund was born in Warsaw on 26 December 1900. He entered Warsaw University in 1919, he wanted to study astronomy, but since such studies were not offered at that time, he decided to study mathematics. He learned about trigonometric series from Aleksander Rajchman during his seminar on this subject held at the University of Warsaw. In 1922 Zygmund was appointed as a junior assistant at the Chair of Mathematics of Warsaw Polytechnic School. He was promoted to a senior assistant after obtaining PhD in 1923 at the University of Warsaw. Zygmund made his habilitation in 1926 and in 1930 was offered a Chair of Mathematics of Stefan Batory University in Wilno, where he worked until the Second World War in 1939. There he encountered Józef Macinkiewicz who was then a freshly enrolled student. Their collaboration lasted until 1939. In 1940 Zygmund managed to leave Poland for the United States, where he was first appointed a visiting professor in MIT and later obtained a position of an assistant professor at the Mount Holyoke College. In 1945 he moved to the University of Pennsylvania in Philadelphia and two years later to the University of Chicago. He spent in Chicago the rest of his life and died there on 30 May 1992.
The list of publications of Antoni Zygmund counts 215 positions, the last one is article on Aleksander Rajchman.
We quote now from two articles on Zygmund's "Trigonometric Series" published in the Bulletin of the American Mathematical Society, vol 37. The first concerns the first edition of the book (1935), and the other the second edition (1959).
'' It has been a repeated privilege of the reviewer to express his appreciation of the high standards and excellent quality of the series of monographs of which Volume V is now under his consideration. Each volume of the series published so far represents an important event in the development of mathematical research, and the present volume in this respect is second to none of its predecessors. If one looks through the long list of books on Fourier series one can not help feeling that even the bulkiest them are far giving an adequate picture of the present status of the field. The non-existence of a monograph giving such a picture was very badly felt not only by the beginners but also by specialist, and the failure of so many attempts to write a real book on Fourier series created an impression that the task was almost hopeless. The author of the present monograph completely succeeded in dispelling this "inferiority complex" and produced a book which not only introduces the reader into the immense field the theory of Fourier series but at the same time almost imperceptibly brings him to the latest achievements, many of them being due author himself. The style of the book is rigorous and vigorous and the exposition elegant and clear to smallest details.''
'' In his course at the University of Cambridge, Professor Littewood used to call the first edition of Zygmund's book ''the Bible''. This second edition, coming almost twenty-five years after the first one, will undoubtedly deserve this name even more, not only because it takes into account the work done in the field during this period, but also because the author, profiting from new experience and constant reflection on his past work, has introduced many topics which had been aside in the first edition.
The book is dedicated to the memories of two polish [sic] mathematicians, A. Rajchman and J. Marcinkiewicz, who met both with a tragic end during the last word war: Rajchman was executed by the Nazis, while Marcinkiewicz died under circumstances not yet fully explained. The first one Zygmund calls "his teacher", the second one "his pupil", but both have considerably influenced the mathematical thought of Zygmund, who had an equal respect to the genius of these two mathematicians of the celebrated Polish school.''
Reference: Selected Papers of Antoni Zygmund, Kluver Academic Publishers, 1989.
See also Zygmunt page of University of St. Andrews