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Some footprints of Marcinkiewicz in summability theory

Ferenc Weisz (2011)

Banach Center Publications

Four basic results of Marcinkiewicz are presented in summability theory. We show that setting out from these theorems many mathematicians have reached several nice results for trigonometric, Walsh- and Ciesielski-Fourier series.

Strong summability of Ciesielski-Fourier series

Ferenc Weisz (2004)

Studia Mathematica

A strong summability result is proved for the Ciesielski-Fourier series of integrable functions. It is also shown that the strong maximal operator is of weak type (1,1).

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