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Marcinkiewicz interpolation theorem and Marcinkiewicz spaces
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2012 (English)In: Wiadomosci Matematyczne, ISSN 2080-5519, Vol. 48, no 2, 157-171 p.Article in journal (Refereed) Published
Abstract [en]

Józef Marcinkiewicz (1910-1940) was one of the most eminent figures in Polish mathematics and together with Stanislaw Zaremba, Leon Lichtenstein, Juliusz Schauder and Antoni Zygmund, the most prominent in analysis. Zygmund considered him as his best pupil, although he had many students in Poland and the USA. We must also remember that it is because of the Master, who was Zygmund, Marcinkiewicz also became a known mathematician. Marcinkiewicz wrote 55 scientific papers in six years (1933-1939) and his name in mathematics is connected with the Marcinkiewicz interpolation theorem, Marcinkiewicz spaces, the Marcinkiewicz integral and Marcinkiewicz function, the Marcinkiewicz multiplier theorem, the Jessen-Marcinkiewicz-Zygmund strong differentiation theorem, Marcinkiewicz-Zygmund vector-valued inequalities, Marcinkiewicz-Zygmund inequalities in probability, the Marcinkiewicz-Zygmund strong law of large numbers, Marcinkiewicz-Zygmund inequalities for trigonometric functions and polynomials, the Grünwald-Marcinkiewicz interpolation theorem, the Marcinkiewicz-Salem conjecture, the Marcinkiewicz theorem on the characteristic function, the Marcinkiewicz test for pointwise convergence of Fourier series, the Marcinkiewicz theorem on the Haar system, the Marcinkiewicz theorem on universal primitive functions and the Marcinkiewicz theorem on the Perron integral. The first two parts from these achievements are presented and the description of other parts can be found in the recent paper of Maligranda [LM11]. Finally, in the third part, the life, scientific career, work and tragic end of Józef Marcinkiewicz is presented.

Place, publisher, year, edition, pages
2012. Vol. 48, no 2, 157-171 p.
Research subject
URN: urn:nbn:se:ltu:diva-9985Local ID: 8b95b707-84a0-4f08-aec1-63fb64893c6bOAI: diva2:982924
Validerad; 2012; 20121015 (evan)Available from: 2016-09-29 Created: 2016-09-29Bibliographically approved

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