Józef Marcinkiewicz (1910–1940) – on the centenary of his birth

Abstract

Abstract. Józef Marcinkiewicz's (1910Marcinkiewicz's ( -1940 name is not known by many people, except maybe a small group of mathematicians, although his influence on the analysis and probability theory of the twentieth century was enormous. This survey of his life and work is in honour of the 100 th anniversary of his birth and 70 th anniversary of his death. The discussion is divided into two periods of Marcinkiewicz's life. First, 1910First, -1933, that is, from his birth to his graduation from the University of Stefan Batory in Vilnius, and for the period 1933-1940, when he achieved scientific titles, was working at the university, did his army services and was staying abroad. Part 3 contains a list of different activities to celebrate the memory of Marcinkiewicz. In part 4, scientific achievements in mathematics, including the results associated with his name, are discussed. Marcinkiewicz worked in functional analysis, probability, theory of real and complex functions, trigonometric series, Fourier series, orthogonal series and approximation theory. He wrote 55 scientific papers in six years (1933)(1934)(1935)(1936)(1937)(1938)(1939). Marcinkiewicz's name in mathematics is connected with the Marcinkiewicz interpolation theorem, Marcinkiewicz spaces, the Marcinkiewicz integral and function, Marcinkiewicz-Zygmund inequalities, the Marcinkiewicz-Zygmund strong law of large numbers, the Marcinkiewicz multiplier theorem, the Marcinkiewicz-Salem conjecture, the Marcinkiewicz theorem on the characteristic function and the Marcinkiewicz theorem on the Perron integral. Books and papers containing Marcinkiewicz's mathematical results are cited in part 4 just after the discussion of his mathematical achievements. The work ends with a full list of Marcinkiewicz's scientific papers and a list of articles devoted to him.

Permutations, Signs, and Sum Ranges

“…(a0) follows at once from the observation that lim n x n 2 = 0. (a1) First, we reproduce the corresponding fragment from (p. 173, [34]): since…”

Some remarks and documents concerning the emigration of Polish mathematicians during the 1930s and early 1940s

“…Stefan Kempisty (1892Kempisty ( -1940 committed suicide in prison in 1940 during Soviet occupation which began in June 1940 and ended in 1941 when the Germans invaded Lithuania (Józwik, Maligranda, Terepeta 2017). While Zygmund reached the US in 1940 and founded an influential analytical school there (see the quote by his students given above), his student Józef Marcinkiewicz was killed as a Polish military officer in Soviet captivity (Maligranda 2011). Roughly speaking the situation is as follows.…”

“…Ciesielska, Maligranda 2014;Maligranda 2011 andDuda 2012. The latter publication comprises many more refugees than those from Nazi oppression, but -maybe for lack of space -it basically refrains from giving historical analysis.…”

“…Steinhaus in his diaries of January 1945 already counted 26 murdered, two among them killed by the Soviets (Kempisty, who committed suicide when jailed by the Russians in Wilno, and Marcinkiewicz). For Marcinkiewicz seeMaligranda 2011. See also the list inKuratowski 1980 (pp.…”

Maximal function in Beurling–Orlicz and central Morrey–Orlicz spaces

“…Second, it is well-known that the maximal operator M is of weak-type (1, 1) (this was proved in 1939 independently by Wiener [W] and Marcinkiewicz-Zygmund-see [M3,Theorem 15,p. 196]), that is, there exists a constant C 3 > 1 such that ( 10) [Gr,Theorem 2.1.6] proved (10) with the constant C 3 being at most 3 n .…”