We prove the almost everywhere convergence of the Marcinkiewicz means of integrable functions σₙf → f for every f ∈ L¹(I²), where I is the group of 2-adic integers.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-3-3, author = {I. Blahota and G. G\'at}, title = {Almost everywhere convergence of Marcinkiewicz means of Fourier series on the group of 2-adic integers}, journal = {Studia Mathematica}, volume = {192}, year = {2009}, pages = {215-222}, zbl = {1172.42009}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-3-3} }
I. Blahota; G. Gát. Almost everywhere convergence of Marcinkiewicz means of Fourier series on the group of 2-adic integers. Studia Mathematica, Tome 192 (2009) pp. 215-222. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-3-3/