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Józef Marcinkiewicz (1910–1940) – on the centenary of his birth. (English) Zbl 1239.01097

Nawrocki, Marek (ed.) et al., Marcinkiewicz centenary volume. Proceedings of the Józef Marcinkiewicz centenary conference, June 28–July 2, 2010. Warszawa: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-14-0/pbk). Banach Center Publications 95, 133-234 (2011).
This paper of book size is a survey covering the life of and mathematics done by Józef Marcinkiewicz (1910–1940), a great mathematical talent who died before time. He graduated in 1933 from the Vilnius University (then within borders of Poland) and spent the year 1933/34 in military service. His scientific life fell thus within 6 years only, from 1934 to 1940 when, being a prisoner of war in Soviet captivity, he was shot by them. But his scientific influence has been enormous. In that short period he was regularly called up to military training (acquiring officer’s rank in 1938), spent the year 1935–36 in Lvov and the year 1938/39 in Paris and London, and still he managed to write then over 50 papers most of which are still of value and exert a standing influence. Major part of the paper is a review of it.
The review is divided into 6 chapters: Functional Analysis, Probability Theory, Real Mathematical Analysis, Fourier Series and Orthogonal Series, Approximation Theory, Some Other Marcinkiewicz’s Results. And in turn each chapter is subdivided into subchapters. E.g., the chapter on Functional Analysis is subdivided into: Marcinkiewicz interpolation theorem, Marcinkiewicz function and sequence spaces, Marcinkiewicz \(M^p(\mathbb{R})\) spaces, Marcinkiewicz-Zygmund vector-valued inequalities, rearrangement of series – Marcinkiewicz’s example. The mere number of chapters and subchapters together with their titles give an insight into the versatility of Marcinkiewicz’s talent. But the author offers much more: each subchapter presents the main results obtained by Marcinkiewicz in the area, the presentation being followed by a list of books and papers using or extending those results. To check the degree of the the author’s penetration, the reviewer has summed up those lists: in total they contain more than 530 items! The article is completed by the list of all publications of Marcinkiewicz, the list of 26 papers bringing some information on him (including his Collected Works, published in 1964) and the list of 23 general “References”. A great impressive work, abundantly illustrated and showing well the grandeur of talent and the versatility of Józef Marcinkiewicz.
For the entire collection see [Zbl 1234.00021].

MSC:

01A70 Biographies, obituaries, personalia, bibliographies
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46B70 Interpolation between normed linear spaces
28A15 Abstract differentiation theory, differentiation of set functions
60E15 Inequalities; stochastic orderings
46B09 Probabilistic methods in Banach space theory
60E10 Characteristic functions; other transforms
60F15 Strong limit theorems
42B15 Multipliers for harmonic analysis in several variables
26D05 Inequalities for trigonometric functions and polynomials
41A10 Approximation by polynomials
26D15 Inequalities for sums, series and integrals
01A60 History of mathematics in the 20th century

Biographic References:

Marcinkiewicz, Józef
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