Convergence of Marcinkiewicz Means of Integrable Functions with Respect to Two-Dimensional Vilenkin Systems
Convergence of Marcinkiewicz Means of Integrable Functions with Respect to Two-Dimensional...
Gát, György
2004-09-01 00:00:00
We prove that the maximal operator of the Marcinkiewicz mean of integrable two-variable functions is of weak type (1, 1) on bounded two-dimensional Vilenkin groups. Moreover, for any integrable function 𝑓 the Marcinkiewicz mean ॣ 𝑛 𝑓 converges to 𝑓 almost everywhere.
http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.pngGeorgian Mathematical Journalde Gruyterhttp://www.deepdyve.com/lp/de-gruyter/convergence-of-marcinkiewicz-means-of-integrable-functions-with-MTBpmOouyH
Convergence of Marcinkiewicz Means of Integrable Functions with Respect to Two-Dimensional Vilenkin Systems
We prove that the maximal operator of the Marcinkiewicz mean of integrable two-variable functions is of weak type (1, 1) on bounded two-dimensional Vilenkin groups. Moreover, for any integrable function 𝑓 the Marcinkiewicz mean ॣ 𝑛 𝑓 converges to 𝑓 almost everywhere.
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